approximation of biholomorphic mappings by automorphisms of cn in this paper we prove several results on approximation of biholomorphic mappings between domains in c n 2 by holomorphic automorphisms of c recall that the group of holomorphic automorphisms of c denoted aut c consists of those holomorphic mappings c c that have a holomorphic inverse 4 1 c c with the topology of uniform convergence on compact sets aut c is a topological group while the group aut c 1 of automorphisms of the complex plane consists only of the linear mappings az b a b e c a 4 0 the group aut c is very large and complicated when n 2 let us choose a linear coordinate system on c and write the coordinates as z z w where z z1 zn i c c n 1 and w z c then autc n contains mappings of the form

algebraic volume density property of affine algebraic manifolds we introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it in particular that it implies the volume density property the main results of the paper are producing two big classes of examples of stein manifolds with volume density property one class consists of certain affine modifications of n equipped with a canonical volume form the other is the class of all linear algebraic groups equipped with the left invariant volume form

positivity of character subbundles and minimum principle for noncompact group actions based on the results of berndtsson on the positivity of holomorphic vector bundles associated to holomorphic fibration we prove that under the setting of the compact lie group actions the character subbundles of such bundles are holomorphic vector bundles and positive in the sense of nakano the second main purpose of the present paper is to establish berndtsson s integral form of kiselman s minimum principle in the setting of the noncompact lie group actions

an oka principle for equivariant isomorphisms let g be a reductive complex lie group acting holomorphically on normal stein spaces x and y which are locally g biholomorphic over a common categorical quotient q when is there a global g biholomorphism x y if the actions of g on x and y are what we with justification call generic we prove that the obstruction to solving this local to global problem is topological and provide sufficient conditions for it to vanish our main tool is the equivariant version of grauert s oka principle due to heinzner and kutzschebauch we prove that x and y are g biholomorphic if x is k contractible where k is a maximal compact subgroup of g or if x and y are smooth and there is a g diffeomorphism x y over q which is holomorphic when restricted to each fibre of the quotient map x q we prove a similar theorem when is only a g homeomorphism but with an assumption about its action on g finite functions when g is abelian we obtain stronger theorems our results can be interpreted as instances of the oka principle for sections of the sheaf of g biholomorphisms from x to y over q this sheaf can be badly singular even for a low dimensional representation of sl2 our work is in part motivated by the linearisation problem for actions on n it follows from one of our main results that a holomorphic g action on n which is locally g biholomorphic over a common quotient to a generic linear action is linearisable

infinite dimensionality of the automorphism groups of homogeneous stein manifolds we show that the group rm aut mathcal o x of holomorphic automorphisms of a stein manifold x with dim x 2 is infinite dimensional provided x is a homogeneous space of a holomorphic action of a complex lie group

integration of navier stokes equations using dual time stepping and a multigrid method efficient acceleration techniques typical of explicit steady state solvers are extended to tune accurate calcu lations stability restrictions are greatly reduced by means of a fully implicit time discretization a four stage runge kutta scheme with local tune stepping residual smoothing and multigridding is used instead of traditional computationally expensive factorizations two applications to natural unsteady viscous flows are presented to check for the capability of the procedure ecent progress in computational fluid dynamics along with the evolution of computer performance encourages scientists to look in to details of flow physics there are practical applications where the unsteadiness of the problem can not be neglected i e vortex shedding natural unsteadiness forced unsteadiness aeroe lasticity turbomachinery rotor stator interaction up to now most of the analysis and designing tools are based on a steady or quasi steady assumption even if the flow is known to be unsteady today due to the improvement in computer resources there is a strong interest in developing methodologies for efficient and reliable sim ulation of unsteady flow features it is a common experience while using time accurate explicit schemes to be forced to choose the time step on the basis of stability restrictions as a consequence unless the problem is a very high frequency one the number of time steps to be performed is much higher than the one required for time accuracy by means of some implicit factorization stability restrictions can be relaxed but the work required at each time step grows rapidly with grid dimension and complexity of the flow equations in addition application of boundary conditions in a fully implicit manner is difficult in viscous flow calculations the grid is clustered close to the shear layer and the characteristic time step varies several orders of mag nitude inside the computational domain even if in several practical applications the characteristic time step of the core flow region is comparable with the one required by time accuracy close to the walls the time step restrictions become extremely severe there fore highly vectorizable schemes with less stability restrictions on the allowable time step would be an interesting combination explicit schemes combined with acceleration techniques have proven to be very effective for solving steady problems 1 3 unfortu nately the computational efficiency of those time marching solvers is achieved by sacrificing the accuracy in time in this paper it is shown that the conventional steady state acceleration techniques specifically the multigrid techniques can still be applied to unsteady viscous problems the basic idea is to introduce a dual time stepping and to reformulate the governing equations so that they can be han dled by an explicit accelerated scheme 4 if the time discretization is made implicit stability restrictions are removed and accelera tion techniques can be used instead of traditional time consuming factorizations i e alternate directional implicit and lower upper

pointwise topology on completely distributive lattices abstract in this paper the author presents a kind of pointwise topology theory on complete completely distributive lattices which is both a generalization of fuzzy topology and a further generalization of the author s papers 14 15

prediction of nonequilibrium turbulent flows with explicit algebraic stress models an explicit algebraic stress equation developed by gatski and speziale is used in the framework of the k uj and k e formulations to predict two dimensional separated turbulent flows the nonequilibrium effects are modeled through coefficients that depend nonlinearly on both rotational and irrotational strains the proposed models were implemented in the courant friedrichs lewy three dimensional navier stokes code comparisons with the experimental data are presented which clearly demonstrate that explicit algebraic stress models improve the response of standard two equation models to nonequilibrium effects i introduction

criteria for the density property of complex manifolds in this paper we suggest new effective criteria for the density property this enables us to give a trivial proof of the original anders en lempert result and to establish almost free of charge the algebraic density property for all linear algebraic groups whose connected components are different from tori or c as another application of this approach we tackle the question asked among others by f forstneri v c about the density of algebraic vector fields on euclidean space vanishing on a codimension 2 subvariety

the cardinal functions on l fuzzy topological spaces in this paper we first introduce a series of concepts of the cardinal functions on l fuzzy topological spaces then we obtain some elementary cardinal inequalities on l fuzzy topological spaces finally we solve a difficult problem in the cardinal functions of l fuzzy topological spaces

holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space we construct holomorphic families of proper holomorphic embeddings of mathbb c k into mathbb c n 0 textless k textless n 1 so that for any two different parameters in the family no holomorphic automorphism of mathbb c n can map the image of the corresponding two embeddings onto each other as an application to the study of the group of holomorphic automorphisms of mathbb c n we derive the existence of families of holomorphic mathbb c actions on mathbb c n n ge5 so that different actions in the family are not conjugate this result is surprising in view of the long standing holomorphic linearization problem which in particular asked whether there would be more than one conjugacy class of mathbb c actions on mathbb c n with prescribed linear part at a fixed point

complex analytic quotients of algebraic g varieties it is shown that any compact semistable quotient of a normal variety by a complex reductive lie group g in the sense of heinzner and snow is a good quotient this reduces the investigation and classification of such complex analytic quotients to the corresponding questions in the algebraic category as a consequence of our main result we show that every compact space in nemirovski s class fancyscript q g has a realisation as a good quotient and that every complete algebraic variety in fancyscript q g is unirational with finitely generated cox ring and at worst rational singularities in particular every compact space in class fancyscript q t where t is an algebraic torus is a toric variety

an equivariant version of grauert s oka principle for example a theorem of oka asserts that every holomorphic line bundle over a domain of holomorphy in 12 is holomorphicaily trivial if and only if it is topologically trivial in g3 grauer t proves that the category of bundles over a stein space x with a complex lie group as a structure group is the same up to isomorphism if considered in the topological or complex analytic category we would like to underl ine that grauert s method of proof also has far reaching consequences see e g fr1 fr2 in this article we prove the equivariant version of grauert s oka principle for a compact lie group of holomorphic t ransformations on x the precise statements can be found in w w and w for example as a consequence of the main results we obtain

a new notion of tameness abstract we generalize the notion of tame discrete sets introduced by rosay and rudin from complex euclidean space to arbitrary complex manifolds and establish their basic properties we show that complex linear algebraic groups different from the complex line or the punctured complex line contain tame discrete sets

algebraic volume density property for affine homogeneous spaces let x be a connected affine homogenous space of a linear algebraic group g over mathbb c 1 if x is different from a line or a torus we show that the space of all algebraic vector fields on x coincides with the lie algebra generated by complete algebraic vector fields on x 2 suppose that x has a g invariant volume form omega we prove that the space of all divergence free with respect to omega algebraic vector fields on x coincides with the lie algebra generated by divergence free complete algebraic vector fields on x including the cases when x is a line or a torus the proof of these results requires new criteria for algebraic volume density property based on so called module generating pairs

maximal complexifications of certain homogeneous riemannian manifolds let m g k be a homogeneous riemannian manifold with dim c g c dim r g where g c denotes the universal complexification of g under certain extensibility assumptions on the geodesic flow of m we give a characterization of the maximal domain of definition in tm for the adapted complex structure and show that it is unique for instance this can be done for generalized heisenberg groups and naturally reductive homogeneous riemannian spaces as an application it is shown that the case of generalized heisenberg groups yields examples of maximal domains of definition for the adapted complex structure which are neither holomorphically separable nor holomorphically convex

compact kahler quotients of algebraic varieties and geometric invariant theory abstract given an action of a complex reductive lie group g on a normal variety x we show that every analytically zariski open subset of x admitting an analytic hilbert quotient with projective quotient space is given as the set of semistable points with respect to some g linearised weil divisor on x applying this result to hamiltonian actions on algebraic varieties we prove that semistability with respect to a momentum map is equivalent to git semistability in the sense of mumford and hausen it follows that the number of compact momentum map quotients of a given algebraic hamiltonian g variety is finite as further corollary we derive a projectivity criterion for varieties with compact kahler quotient

density property for hypersurfaces uv p bar x we study hypersurfaces of mathbb c n 2 bar x u v given by equations of form uv p bar x where the zero locus of a polynomial p is smooth reduced the main result says that the lie algebra generated by algebraic completely integrable vector fields on such a hypersurface coincides with the lie algebra of all algebraic vector fields consequences of this result for some conjectures of affine algebraic geometry and for the oka grauert gromov principle are discussed

invariant rings and quasiaffine quotients we study hilbert s fourteenth problem from a geometric point of view nagata s celebrated counterexample demonstrates that for an arbitrary group action on a variety the ring of invariant functions need not be isomorphic to the ring of functions of an affine variety in this paper we will show that nevertheless it is always isomorphic to the ring of functions on a quasi affine variety

oka s principle for holomorphic sections of elliptic bundles 2 the h principle for locally trivial fibrations 2 1 the h principle over small subsets 2 2 the h principle over totally real submanifolds 2 3 local extension of the h principle 2 4 localizable extensions 2 5 the h principle for cm bundles 2 6 manifolds with totally real souls 2 7 totally real extensions 2 8 nicely localizable extensions 2 9 the basic h principle for z x 2 10 homomorphisms and holomorphic maps of rank r

free dense subgroups of holomorphic automorphisms we show the existence of free dense subgroups generated by two elements in the holomorphic shear and overshear group of complex euclidean space and extend this result to the group of holomorphic automorphisms of stein manifolds with the density property provided there exists a generalized translation the conjugation operator associated to this generalized translation is hypercyclic on the topological space of holomorphic automorphisms

the moduli space of fano manifolds with kahler ricci solitons abstract we construct a canonical hausdorff complex analytic moduli space of fano manifolds with kahler ricci solitons this enlarges the moduli space of fano manifolds with kahler einstein metrics we discover a moment map picture for kahler ricci solitons and give complex analytic charts on the topological space consisting of kahler ricci solitons by studying differential geometric aspects of this moment map some stacky words and arguments on gromov hausdorff convergence help to glue them together in the holomorphic manner

positivity of direct images of positively curved volume forms we discuss kiselman berndtsson s minimum principle for plurisubharmonic functions in terms of the positivity of direct images of certain positively curved volume forms and generalize it to holomorphically convex manifolds with compact group actions with this generalization and other techniques we establish a minimum principle for positively curved volume forms from the point of view of geometric invariant theory on stein manifolds minimum principle with some noncompact group actions is also considered

flexible varieties and automorphism groups given an irreducible affine algebraic variety x of dimension n 2 we let saut x denote the special automorphism group of x that is the subgroup of the full automorphism group aut x generated by all one parameter unipotent subgroups we show that if saut x is transitive on the smooth locus x reg then it is infinitely transitive on x reg in turn the transitivity is equivalent to the flexibility of x the latter means that for every smooth point x x reg the tangent space t x x is spanned by the velocity vectors at x of one parameter unipotent subgroups of aut x we also provide various modifications and applications

accurate numerical simulation of compressible transitional flows in turbomachinery an accurate and efe cient methodology is provided for computing turbulent and transitional e ows by solving the compressible reynolds averaged navier stokes equations with an explicit algebraic stress model and k turbulence closure the space discretization is based on a e nite volume method with roe s approximate riemann solver and formally second order accurate muscl extrapolation second order accuracy in time is achieved using a dual time stepping technique combined with an explicit runge kutta scheme and multigrid acceleration to converge the false transient at each physical time level the turbulence model has been validated computing the vortex shedding behind a two dimensional turbine cascade furthermore the transition model of mayle for separated e ow has been combined with such a turbulence model this methodology has been validated computing thee owthroughthet106low pressureturbinecascadewithseparated e owtransitionatthesuction sideboundary layer finally thethree dimensionale owthroughthet106linearcascadehasbeencomputedprovidingtheanalysis of the loss coefe cient distribution downstream of the cascade and the description of the interaction between the secondary e ow pattern and the suction side separation bubble

algebraic density property of danilov gizatullin surfaces a danilov gizatullin surface is an affine surface v which is the complement of an ample section s for the ruling of a hirzebruch surface the remarkable theorem of danilov and gizatullin states that the isomorphism class of v depends only on the self intersection number s s in this paper we apply the theorem of danilov gizatullin to prove that the lie algebra generated by the complete algebraic vector fields on v coincides with the set of all algebraic vector fields of v