local properties of j complex curves in lipschitz continuous structures we prove the existence of primitive curves and positivity of intersections of j complex curves for lipschitz continuous almost complex structures these results are deduced from the comparison theorem for j holomorphic maps in lipschitz structures previously known for j of class mathcal c 1 lip we also give the optimal regularity of curves in lipschitz structures it occurs to be mathcal c 1 lnlip i e the first derivatives of a j complex curve for lipschitz j are log lipschitz continuous a simple example that nothing better can be achieved is given further we prove the genus formula for j complex curves and determine their principal puiseux exponents all this for lipschitz continuous j s

self duality equations for ginzburg landau and seiberg witten type functionals with 6th order potentials the abelian chern simons higgs model of hong kim pac and jackiw weinberg leads to a ginzburg landau type functional with a 6th order potential on a compact riemann surface we derive the existence of two solutions with different asymptotic behavior as the coupling parameter tends to 0 for any number of prescribed vortices we also introduce a seiberg witten type functional with a 6th order potential and again show the existence of two asymptotically different solutions on a compact kahler surface the analysis is based on maximum principle arguments and applies to a general class of scalar equations

factorization homology i higher categories abstract we construct a pairing which we call factorization homology between framed manifolds and higher categories the essential geometric notion is that of a vari framing of a stratified manifold which is a framing on each stratum together with a coherent system of compatibilities of framings along links between strata our main result constructs labeling systems on disk stratified vari framed n manifolds from n categories these n categories in contrast with the literature to date are not required to have adjoints this allows the following conceptual definition the factorization homology m c of a framed n manifold m with coefficients in an n category c is the classifying space of c labeled disk stratifications over m the core calculation underlying our main result is the following for any disk stratified manifold the space of conically smooth diffeomorphisms which preserve a vari framing is discrete

a new mixed basis navier stokes formulation for incompressible flows over complex geometries numerical modeling of complex geometries necessitates the use of curvilinear body fitted coordinates this article proposes a novel mixed basis formulation of the governing conservation equations for general curvilinear non orthogonal grids with the physical covariant velocity as the primary solution variable this results in an algorithm which has many advantages of orthogonal equations the conservation equations written in this form retains the diagonal dominance of the pressure equation the newly formed conservation equations are solved on a structured grid using the simpler algorithm and are shown to converge well for non orthogonal grids standard k model is used for the turbulence closure

calderon zygmund estimates and non uniformly elliptic operators abstract we consider a class of non uniformly nonlinear elliptic equations whose model is given by div d u p 2 d u a x d u q 2 d u div f p 2 f a x f q 2 f where p q and a x 0 and establish the related nonlinear calderon zygmund theory in particular we provide sharp conditions under which the natural and optimal calderon zygmund type result f p a x f q l loc d u p a x d u q l loc holds for every 1 these problems naturally emerge as euler lagrange equations of some variational integrals introduced and studied by marcellini 41 and zhikov 53 in the framework of homogenisation and lavrentiev phenomenon

dissolving four manifolds and positive scalar curvature we prove that many simply connected symplectic four manifolds dissolve after connected sum with only one copy of s2 s2 for any finite group g that acts freely on the three sphere we construct closed smooth four manifolds with fundamental group g which do not admit metrics of positive scalar curvature but whose universal covers do admit such metrics

regularity for double phase variational problems we prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases according to the zero set of a modulating coefficient a cdot the model case is given by the functional w mapsto int dw p a x dw q rm d x where q p and a cdot geqq 0

knots links and 4 manifolds in this paper we investigate the relationship between isotopy classes of knots and links in s and the di eomorphism types of homeomorphic smooth 4 manifolds as a corollary of this initial investigation we begin to uncover the surprisingly rich structure of di eomorphism types of manifolds homeomorphic to the k3 surface in order to state our theorems we need to view the seiberg witten invariant of a smooth 4 manifold as a multivariable laurent polynomial to do this recall that the seiberg witten invariant of a smooth closed oriented 4 manifold x with b2 x 1 is an integer valued function which is de ned on the set of spinc structures over x cf w km ko1 t1 in case h1 x z has no 2 torsion which will be the situation in this paper there is a natural identi cation of the spinc structures of x with the characteristic elements of h2 x z in this case we view the seiberg witten invariant as

a stability property of symplectic packing we prove that for any closed symplectic 4 manifold m with h 2 m q there exists a number n 0 such that for every n n 0 m admits full symplectic packing by n equal balls we also indicate how to compute this n 0 our approach is based on donaldson s symplectic submanifold theorem and on tools from the framework of taubes theory of gromov invariants

application of wall functions to generalized nonorthogonal curvilinear coordinate systems a method has been developed for the application of wall functions to generalized curvilinear coordinate systems with nonorthogonal grids two test cases have been computed using this method with the k e turbulence model flow over a flat plate at 0 deg angle of attack using a nonorthogonal grid at the wall and flow over a prolate hemispheroid with a hemispherical nose cap at 0 deg angle of attack all results are compared with experimental data in addition the hemispheroid results are compared with computations using the baldwin lomax algebraic turbulence model and the chien low reynolds number k e turbulence model

the derivative of the maximal function in this note we show that the local hardy littlewood maximal operator is bounded in the sobolev space thus the maximal function often has partial derivatives we also show that the maximal operator preserves the zero boundary values in sobolev s sense

regularity of the centered fractional maximal function on radial functions abstract we study the regularity properties of the centered fractional maximal function m more precisely we prove that the map f m f is bounded and continuous from w 1 1 r d to l q r d in the endpoint case q d d if f is a radial function for d 1 the radiality assumption can be removed this corresponds to the counterparts of known results for the non centered fractional maximal function the main new idea consists in relating the centered and non centered fractional maximal function at the derivative level

computation of rotating turbulent flow with an algebraic reynolds stress model la rotation a un effet important sur la structure des ecoulements turbulents les modeles de turbulence bases sur une viscosite tourbillonnaire isotrope ne permettent pas de prevoir de tels ecoulements on propose un modele de contrainte de reynolds algebrique pour modifier la relation de viscosite tourbillonnaire de kolmogorov prandtl de maniere a produire un modele de turbulence anisotrope

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

calderon zygmund estimates for general elliptic operators with double phase abstract we derive calderon zygmund type estimates for the gradient of bounded distributional solutions to the problem div b x u d u p 2 d u a x d u q 2 d u div f p 2 f a x f q 2 f where 1 p q and 0 a c the coefficient b x z is supposed to be small bmo with respect to x and merely continuous in z

convex and concave surface curvature effects in wall bounded turbulent flows a fully ellipitic numerical method developed to solve the two dimensional reynolds averaged navier stokes equations for an incompressible fluid is employed in a computational study of several flows involving convex and concave surface curvature the k epsilon turbulence model and variant of it proposed to improve the calculation of flows with streamline curvature are used in conjunction with a one equation near wall model the performance of the method is examined through computations of fully developed curved duct flow and boundary layers on curved surfaces in each case the main features of the flow are consistently reproduced however the computations tend to overpredict the convex wall skin friction and underpredict the concave wall skin friction

implicit multiple grid solution of the compressible navier stokes equations using k epsilon turbulence closure in the present work an algorithm for the numerical solution of the two dimensional mass weighted ensemble averaged compressible navier stokes equations is presented turbulence closure for the reynolds stresses is obtained using a low reynolds n umber two equation k s model which includes near wall effects the same algorithm is used for the integration of both the navier stokes and the turbulence transport equations the algorithm consists of a basic explicit finite volume scheme whose convergence is accelerated using local time step ping and multiple grid techniques convergence is further enhanced by the use of an implicit residual smoothing technique applied both in the fine and the coarser grids the application of the numerical scheme to the solution of the k s equations is examined in detail comparisons of computations with experimental data are presented for three shock wave turbulent boundary layer interaction flows algorithm convergence rate and cpu time require ments are discussed he numerical solution of the navier stokes equations for the simulation of turbulent flowfields is a subject of intense research and code development work 1 interest is focused both on code applicability to variegated config urations and on computational rapidity although direct simulation of turbulent flows2 or large eddy numerical sim ulations using subgrid turbulence modeling 3 4 have appeared in the literature current status of algorithm development and computer power indicate that for practical applications the ensemble averaged navier stokes equations should be used in conjunction with transport equations for turbulence closure 5 7 algebraic or mixing length models may provide satisfactory results for relatively simple flow geometries8 but require the determination of the shear layer thickness and of the distance of each grid point from the solid boundary thus they lack both geometric invariance and locality which are highly desirable properties from a computational viewpoint when addressing complex flowfields with many interacting solid boundaries although research on reynolds stre ss transport closure appears quite promising 9 10 its extension to three dimensions involves considerable increase of the number of transport equations to be solved also further research con cerning wall effects is required the more so since the use of wall functions is considered inadequate 11 on the other hand the use of two equation closures such as a 12 14 is quite widespread notwithstanding the fact that the use of the boussinesq hypothesis15 introduces a question able simplification of the flow physics 16 the major drawback of the k s model is probably the near wall formulation which fails to reproduce correctly the effects of the solid boundary on turbulence several variants of the original jones launder model12 have been developed in an attempt to improve upon near wall modeling some ten such models have been thor oughly examined in a critical review article by patel et al 17 who concluded that the models of launder and sharma 14

endpoint sobolev and bv continuity for maximal operators abstract in this paper we investigate some questions related to the continuity of maximal operators in w 1 1 and bv spaces complementing some well known boundedness results letting m be the one dimensional uncentered hardy littlewood maximal operator we prove that the map f m f is continuous from w 1 1 r to l 1 r in the discrete setting we prove that m b v z b v z is also continuous for the one dimensional fractional hardy littlewood maximal operator we prove by means of counterexamples that the corresponding continuity statements do not hold both in the continuous and discrete settings and for the centered and uncentered versions

near wall turbulence models for complex flows including separation results of a computational experiment designed to investigate the performance of different near wall treatments in a single turbulence model with a common numerical method are reported the complete fully elliptic reynoldsaveraged navier stokes equations have been solved using a low reynolds number model a new two layer model and a two point wall function method in thek s turbulence model for the boundary layer and wake of two axisymmetric bodies these tests enable the evaluation of the performance of the different approaches in flows involving longitudinal and transverse surface curvatures streamwise and normal pressure gradients viscous inviscid interaction and separation the two layer approach has been found to be quite promising for such flows and can be extended to other complex flows

regularity results for vectorial minimizers of a class of degenerate convex integrals abstract we establish the higher differentiability and the higher integrability for the gradient of vectorial minimizers of integral functionals with p q growth conditions we assume that the non homogeneous densities are uniformly convex and have a radial structure with respect to the gradient variable only at infinity the results are obtained under a possibly discontinuous dependence on the spatial variable of the integrand

on the regularity of maximal operators supported by submanifolds abstract we prove that the maximal operators supported by submanifolds are bounded and continuous on the triebel lizorkin spaces f s p q r d and besov spaces b s p q r d for 0 s 1 and 1 p q as a corollary we also show that these operators are bounded and continuous on the fractional sobolev spaces w s p r d for 0 s 1 and 1 p our main results represent significant improvements as well as natural extensions of what was known previously

existence of renormalized solutions to elliptic equation in musielak orlicz space abstract we prove existence of renormalized solutions to general nonlinear elliptic equation in musielak orlicz space avoiding growth restrictions namely we consider div a x u f l 1 on a lipschitz bounded domain in r n the growth of the monotone vector field a is controlled by a generalized nonhomogeneous and anisotropic n function m the approach does not require any particular type of growth condition of m or its conjugate m neither 2 nor 2 the condition we impose is log holder continuity of m which results in good approximation properties of the space the proof of the main results uses truncation ideas the young measures methods and monotonicity arguments

almost kahler forms on rational 4 manifolds we study nakai moishezon type question and donaldson s tamed to compatible question for almost complex structures on rational four manifolds by extending taubes subvarieties current form technique to j nef genus 0 classes we give affirmative answers of these two questions for all tamed almost complex structures on s 2 bundles over s 2 as well as for many geometrically interesting tamed almost complex structures on other rational four manifolds including the del pezzo ones

prediction of curved channel flow with an extended k epsilon model of turbulence a l aide d une approximation algebrique pour les equations de contraintes de reynolds on calcule une expression plus generale pour le coefficient c de l equation de viscosite turbulente qui rend compte simultanement des effets de courbure de ligne de courant et de la deformation due a la pression dans l ecoulement le dernier incluant les effets d amortissement a la paroi

on the orders of periodic diffeomorphisms of 4 manifolds this paper initiated an investigation on the following question sup pose a smooth 4 manifold does not admit any smooth circle actions does there exist a constant c 0 such that the manifold support no smooth zp actions of prime order for p c we gave affirmative results to this question for the case of holomorphic and symplectic actions with an interesting finding that the constant c in the holomorphic case is topological in nature while in the symplectic case it involves also the smooth structure of the manifold

pointwise behaviour of m1 1 sobolev functions our main objective is to study hajlasz type sobolev functions with the exponent one on metric measure spaces equipped with a doubling measure we show that a discrete maximal function is bounded in the hajlasz space with the exponent one this implies that every such function has lebesgue points outside a set of capacity zero we also show that every hajlasz function coincides with a holder continuous hajlasz function outside a set of small hausdorff content our proofs are based on sobolev space estimates for maximal functions

harnack inequalities for double phase functionals we prove a harnack inequality for minimisers of a class of non autonomous functionals with non standard growth conditions they are characterised by the fact that their energy density switches between two types of different degenerate phases

continuous solutions of nonlinear cauchy riemann equations and pseudoholomorphic curves in normal coordinates we establish elliptic regularity for nonlinear inhomogeneous cauchy riemann equations under weak assumptions and give a counterexample in a borderline case in some cases where the inhomogeneous term has a separable factorization the solution set can be explicitly calculated the methods also give local parametric formulas for pseudoholomorphic curves with respect to some continuous almost complex structures

holder continuity for nonlinear elliptic problem in musielak orlicz sobolev space abstract under appropriate assumptions on the n function the de giorgi process is presented by the tools recently developed in musielak orlicz sobolev space to prove the holder continuity of fully nonlinear elliptic problems as the applications the holder continuity of the minimizers for a class of the energy functionals in musielak orlicz sobolev spaces is proved and furthermore the local holder continuity of the weak solutions for a class of fully nonlinear elliptic equations is provided

sw gr from the seiberg witten equations to pseudo holomorphic curves the purpose of this article is to explain how pseudo holomorphic curves in a symplectic 4 manifold can be constructed from solutions to the seiberg witten equations as such the main theorem proved here theorem 1 3 is an existence theorem for pseudo holomorphic curves this article thus provides a proof of roughly half of the main theorem in the announcement t1 that theorem theorem 4 1 asserts an equivalence between the seiberg witten invariants for a symplectic manifold and a certain gromov invariant which counts with signs the number of pseudoholomorphic curves in a given homology class the seiberg witten invariants were introduced to mathematicians by witten w based on his joint work with nat seiberg sw1 sw2 a description of these invariants is given in section 1 see also km1 t1 suffice it to say here that when x is a compact oriented 4 dimensional manifold with

regularity for minimizers of double phase functionals with mild transition and regular coefficients abstract we prove sharp regularity results for minimizers of the functional p w b x w d w p a x d w p log e d w d x with w w 1 1 p 1 a l a 0 and 0 b l p is a double phase functional with mild transition between d u p and d u p log e d u first under suitable conditions on the moduli of continuity of a and b we prove that local minimizers are of class c 0 for every 0 1 then that they are of class c 1 for some 0 provided the functions a and b are holder continuous

limitations of the near wall k epsilon turbulence model comparisons are given at two different reynolds numbers between the measured turbulent kinetic energy in channel flow and the predictions of several near wall variants of the k e closure included among these are new calculations based on a form of the e equation that is consistent with the physically correct boundary condition it is observed that all of the approaches fail to account for the large peak k value in the wall region that is evident in the experimental data by contrasting the computed energy budget with its measured values it is shown that this defect may be attributed to a fundamental inconsistency in the commonly used model for the pressure diffu sion term in the k equation near the boundary he k e closure is widely utilized today in the prediction of the mean properties of turbulent flowfields in recent years extensions of its basic form have been developed to permit treatment of complex fluid motions such as those found in curved pipes 1 compressible boundary layers 2 com bustion chambers 3 etc a strong incentive for the continued development and application of the k e model has been the remarkable success it has achieved in the prediction of mean velocity fields in wall bounded shear flows such as occur in channels pipes and boundary layers 4 6 the success of the k e closure in these relatively simple flows is not complete however since the high accuracy obtained for mean velocity is not duplicated in the case of the turbulent kinetic energy k a notable defect4 7 9 is the 25 or more underprediction of the large peak k value shown by clark 10 and kreplin and eckelmann11 to occur at y 15 in a channel flow for ap plications where predictions of turbulence levels are impor tant such as in internal combustion engine simulations 12 this failure can be of great practical significance it may be expected that major errors in the prediction of k stem from deficiencies in the low turbulent reynolds number forms of the k e equations which have been developed for the region adjacent to boundaries jones and launder4 for mulated the first such model that permitted k and e to be calculated down to a solid wall without the use of wall func tions several more recent studies including those of lam and bremhorst 7 hassid and poreh 8 and chien 9 have at tempted to improve upon the jones and launder approach but these authors report only modest gains in the accuracy of k the object of the present study is to elucidate the cause of this discrepancy by making direct comparisons between the terms in the exact and modeled energy equations to ac complish this a set of new calculations was performed in which e was required to satisfy the physically correct bound ary condition at the wall it was revealed that the failure of the k e model to predict the correct peak k value is most likely due to reliance on a flawed model for the pressure velocity correlation in the k equation this relation will be shown to be inconsistent with the experimentally measured values of the exact term as found by kreplin and eckelmann 11 and may be directly implicated in suppressing the peak k value removal of this limitation should allow for better predictions of k near solid boundaries

regularity for double phase problems under additional integrability assumptions abstract we study the regularity of quasi minimizers or minimizers of functionals of double phase type in recent years baroni colombo and mingione have investigated regularity theory for bounded minimizers in baroni et al 2015 2018 colombo and mingione 2015 in this paper we assume the minimizers only belong to l space

smooth s cobordisms of elliptic 3 manifolds the main result of this paper states that a symplectic s cobordism of elliptic 3 manifolds is diffeomorphic to a product assuming a canonical contact structure on the boundary based on this theorem we conjecture that a smooth s cobordism of elliptic 3 manifolds is smoothly a product if its universal cover is smoothly a product we explain how the conjecture fits naturally into the program of taubes of constructing symplectic structures on an oriented smooth 4 manifold with b 1 from generic self dual harmonic forms the paper also contains an auxiliary result of independent interest which generalizes taubes theorem sw gr to the case of symplectic 4 orbifolds

standard surfaces and nodal curves in symplectic 4 manifolds continuing the program of ds and u1 we introduce refinements of the donaldson smith standard surface count which are designed to count nodal pseudoholomorphic curves and curves with a prescribed decomposition into reducible components in cases where a corresponding analogue of the gromov taubes invariant is easy to define our invariants agree with those analogues we also prove a vanishing result for some of the invariants that count nodal curves

existence and multiplicity results for double phase problem abstract by variational method we obtain various existence and multiplicity results for the following double phase problem div u p 2 u a x u q 2 u f x u in u 0 on in particular we find a sign changing ground state solution some properties of double phase operator are also obtained

on the variation of maximal operators of convolution type abstract in this paper we study the regularity properties of two maximal operators of convolution type the heat flow maximal operator associated to the gauss kernel and the poisson maximal operator associated to the poisson kernel in dimension d 1 we prove that these maximal operators do not increase the l p variation of a function for any p 1 while in dimensions d 1 we obtain the corresponding results for the l 2 variation similar results are proved for the discrete versions of these operators

weak differentiability for fractional maximal functions of general lp functions on domains abstract let r n be bounded a domain we prove under certain structural assumptions that the fractional maximal operator relative to maps l p w 1 p for all p 1 when the smoothness index 1 in particular the results are valid in the range p 1 n n 1 that was previously unknown as an application we prove an endpoint regularity result in the domain setting

variable exponent functionals in image restoration abstract we study a functional with variable exponent 1 p x 2 which provides a model for image denoising and restoration here p x is defined by the gradient information in the observed image the diffusion derived from the proposed model is between total variation based regularization and gaussian smoothing the diffusion speed of the corresponding heat equation is tuned by the variable exponent p x the minimization problem and its associated flow in a weakened formulation are discussed the existence uniqueness stability and long time behavior of the proposed model are established in the variable exponent functional space w 1 p x experimental results illustrate the effectiveness of the model in image restoration

floer cohomology and pencils of quadrics there is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces we investigate symplectic aspects of this relationship with a view to applications in low dimensional topology

boundedness and unboundedness results for some maximal operators on functions of bounded variation abstract we characterize the space bv i of functions of bounded variation on an arbitrary interval i r in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator m r from bv i into the sobolev space w 1 1 i by restriction the corresponding characterization holds for w 1 1 i we also show that if u is open in r d d 1 then boundedness from bv u into w 1 1 u fails for the local directional maximal operator m t v the local strong maximal operator m t s and the iterated local directional maximal operator m t d m t 1 nevertheless if u satisfies a cone condition then m t s bv u l 1 u boundedly and the same happens with m t v m t d m t 1 and m r

interpolation between holder and lebesgue spaces with applications abstract classical interpolation inequality of the type u x c u y u z 1 is well known in the case when x y z are lebesgue spaces in this paper we show that this result may be extended by replacing norms y or x by suitable holder semi norm we shall even prove sharper version involving weak lorentz norm we apply this result to prove the gagliardo nirenberg inequality for a wider scale of parameters

strong solutions for differential equations in abstract spaces abstract let e f be a locally convex space we denote the bounded elements of e by e b x e x f sup f x in this paper we prove that if b e b is relatively compact with respect to the f topology and f i e b e b is a measurable family of f continuous maps then for each x 0 e b there exists a norm differentiable i e differentiable with respect to the f norm local solution to the initial valued problem u t t f t u t u t 0 x 0 all of this machinery is developed to study the lipschitz stability of a nonlinear differential equation involving the hardy littlewood maximal operator

bounded minimisers of double phase variational integrals bounded minimisers of the functional w mapsto int dw p a x dw q rm d x where 0 leqq a cdot in c 0 alpha and 1 p q are c 1 beta regular provided the sharp bound q leqq p alpha holds

partial regularity for general systems of double phase type with continuous coefficients abstract we consider elliptic systems of double phase problems which satisfy a general structure with continuous coefficients and prove that weak solutions of such systems are holder continuous for any holder exponent 0 1 except for a measure zero set

multiple solutions for a class of double phase problem without the ambrosetti rabinowitz conditions abstract in the present paper in view of the variational approach we consider the existence and multiplicity of weak solutions for a class of the double phase problem div u p 2 u a x u q 2 u f x u in u 0 on where n 2 and 1 p q n firstly by the fountain and dual theorem with cerami condition we obtain some existence of infinitely many solutions for the above problem under some weaker assumptions on f secondly we prove that this problem has at least one nontrivial solution for any parameter 0 small enough and also that the solution blows up in the sobolev norm as 0 finally by imposing additional assumptions on f we establish the existence of infinitely many solutions by using krasnoselskii s genus theory for the above equation

sharp sobolev inequalities in lorentz spaces for a mean oscillation abstract we exhibit the optimal constant for sobolev inequalities in lorentz spaces for a mean oscillation and its relation with a boundedness of the hardy littlewood maximal operator in sobolev spaces some applications to a scale invariant form of hardy s inequality in a limiting case are also considered

sobolev regularity of polar fractional maximal functions abstract we study the sobolev regularity on the sphere s d of the uncentered fractional hardy littlewood maximal operator m at the endpoint p 1 when acting on polar data we first prove that if q d d 0 d and f is a polar w 1 1 s d function we have m f q d f 1 we then prove that the map f m f is continuous from w 1 1 s d to l q s d when restricted to polar data our methods allow us to give a new proof of the continuity of the map f m f from w rad 1 1 r d to l q r d moreover we prove that a conjectural local boundedness for the centered fractional hardy littlewood maximal operator m implies the continuity of the map f m f from w 1 1 to l q in the context of polar functions on s d and radial functions on r d

functions of bounded variation the derivative of the one dimensional maximal function and applications to inequalities we prove that if f i r r is of bounded variation then the uncentered maximal function mf is absolutely continuous and its derivative satisfies the sharp inequality dmf l 1 i df i this allows us to obtain under less regularity versions of classical inequalities involving derivatives

small lefschetz fibrations and exotic 4 manifolds we explicitly construct genus 2 lefschetz fibrations whose total spaces are minimal symplectic 4 manifolds homeomorphic to complex rational surfaces mathbb cp 2 p overline mathbb cp 2 for p 7 8 9 and to 3 mathbb cp 2 q overline mathbb cp 2 for q 12 ldots 19 complementarily we prove that there are no minimal genus 2 lefschetz fibrations whose total spaces are homeomorphic to any other simply connected 4 manifold with b le 3 with one possible exception when b 3 meanwhile we produce positive dehn twist factorizations for several new genus 2 lefschetz fibrations with small number of critical points including the smallest possible example which follow from a reverse engineering procedure we introduce for this setting we also derive exotic minimal symplectic 4 manifolds in the homeomorphism classes of mathbb cp 2 4 overline mathbb cp 2 and 3 mathbb cp 2 6 overline mathbb cp 2 from small lefschetz fibrations over surfaces of higher genera

gromov s compactness theorem for pseudo holomorphic curves we give a complete proof for gromov s compactness theorem for pseudo holomorphic curves both in the case of closed curves and curves with boundary

on the continuous and discontinuous maximal operators abstract in the first part of this paper we study the regularity properties of a wide class of maximal operators these results are used to show that the spherical maximal operator is continuous w 1 p r n w 1 p r n when p n n 1 other given applications include fractional maximal operators and maximal singular integrals on the other hand we show that the restricted hardy littlewood maximal operator m where the supremum is taken over the cubes with radii greater than 0 is bounded from l p r n to w 1 p r n but discontinuous

hurwitz type bound knot surgery and smooth mathbb s 1 four manifolds in this paper we prove several related results concerning smooth mathbb z p or mathbb s 1 actions on 4 manifolds we show that there exists an infinite sequence of smooth 4 manifolds x n n ge 2 which have the same integral homology and intersection form and the same seiberg witten invariant such that each x n supports no smooth mathbb s 1 actions but admits a smooth mathbb z n action in order to construct such manifolds we devise a method for annihilating smooth mathbb s 1 actions on 4 manifolds using fintushel stern knot surgery and apply it to the kodaira thurston manifold in an equivariant setting finally the method for annihilating smooth mathbb s 1 actions relies on a new obstruction we derived in this paper for existence of smooth mathbb s 1 actions on a 4 manifold the fundamental group of a smooth mathbb s 1 four manifold with nonzero seiberg witten invariant must have infinite center we also include a discussion on various analogous or related results in the literature including locally linear actions or smooth actions in dimensions other than four

norms on the cohomology of hyperbolic 3 manifolds we study the relationship between two norms on the first cohomology of a hyperbolic 3 manifold the purely topological thurston norm and the more geometric harmonic norm refining recent results of bergeron engun and venkatesh as well as older work of kronheimer and mrowka we show that these norms are roughly proportional with explicit constants depending only on the volume and injectivity radius of the hyperbolic 3 manifold itself moreover we give families of examples showing that some but not all qualitative aspects of our estimates are sharp finally we exhibit closed hyperbolic 3 manifolds where the thurston norm grows exponentially in terms of the volume and yet there is a uniform lower bound on the injectivity radius

regularity for multi phase variational problems abstract we prove c 1 regularity for local minimizers of the multi phase energy w d w p a x d w q b x d w s d x under sharp assumptions relating the couples p q and p s to the holder exponents of the modulating coefficients a and b respectively

double phase image restoration abstract in this paper we explore the potential of the double phase functional in an image processing context to this end we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained by convergence or relaxation of regularized functionals a central tool is a capped fractional maximal function of the derivative of bv functions

analysis of streamline curvature effects on wall bounded turbulent flows we deal with numerical analysis for the effects of surface curvature particularly the concave curvature on turbulent duct flows and boundary layers a compressible navier stokes code incorporating reynolds stress models has been developed using a four stage runge kutta scheme numerical computations have been carried out for curved flows in 180 deg and 90 deg turning ducts and a turbulent boundary layer using reynolds stress models with without modifications to the dissipation rate e equation various modifications to the e equation are discussed a quantitative relationship has been established between two seemingly different modifications to the e equation it is observed that the modeling of concave curvature effect is qualitatively different from the modeling of convex curvature effect detailed comparisons between computations and data indicate that to capture the strong amplification of turbulence near a concave wall the standard e equation needs to be modified

a space marching method for viscous incompressible internal flows abstract this paper deals with the development of a space marching method for steady incompressible flows the method solves the continuity and the momentum equations as a coupled system at each streamwise station the character of the system of equations is changed from elliptic to hyperbolic parabolic in order to enable the equations to be marched in space the present method has two main advantages compared to the existing parabolic or spacemarching methods for an incompressible flow i it avoids the solution of poisson equations and ii conserves the mass flow without employing any iterative procedure the present method can capture strong secondary velocities and strong transverse pressure gradients predictions of the flow through straight and strongly curved ducts are in good agreement with the analytical and the experimental results