singular kahler einstein metrics we study degenerate complex monge ampere equations of the form omega dd c f n e t f mu where omega is a big semi kahler form on a compact kahler manifold x of dimension n t in r and mu f omega n is a positive measure with density f in l p x omega n p 1 we prove the existence and unicity of continuous o plurisubharmonic solutions in case x is projective and omega psi omega where psi x to v is a proper birational morphism to a normal projective variety omega in ns r v is an ample class and mu has only algebraic singularities we prove that the solution is smooth in the regular locus of the equation we use these results to construct singular kahler einstein metrics of non positive curvature on projective klt pairs in particular on canonical models of algebraic varieties of general type

inequalities and bounds for generalized complete elliptic integrals computable bounds for the generalized complete elliptic integrals of the first and second kind are obtained also bounds for some combinations and products for integrals under discussion are established it has been proven that both families of integrals are logarithmically convex as functions of the first parameter this property has been employed to obtain several inequalities involving integrals in question

on the construction of nadel multiplier ideal sheaves and the limiting behavior of the ricci flow in this note we construct nadel multiplier ideal sheaves using the ricci flow on fano manifolds this extends a result of phong sesum and sturm these sheaves like their counterparts constructed by nadel for the continuity method can be used to obtain an existence criterion for kahler einstein metrics

on stability and the convergence of the kahler ricci flow assuming uniform bounds for the curvature the exponential convergence of the kahler ricci flow is established under two con ditions which are a form of stability the mabuchi energy is bound ed from below and the dimension of the space of holomorphic vector fields in an orbit of the diffeomorphism group cannot jump up in the limit

damage spreading in confined geometries and the influence of boundary conditions a monte carlo study of the ising ferromagnet the spreading of damage in the ising ferromagnet in two dimensional confined geometries of size l m l m close to the critical temperature is studied by means of computer simulations imposing both periodic and open boundary conditions along the m direction the influence of the interfaces between domains of spins having opposite orientation on the spreading of damage can be studied analyzing the spatio temporal evolution of the damage it is found that such interfaces not only considerably speed up the spreading but also cause the enhancement of the damaged area of the sample these statements are based on the evaluation of relevant exponents which characterize the spatio temporal spreading of the damage

scalar curvature and stability of toric varieties we define a stability condition for a polarised algebraic variety and state a conjecture relating this to the existence of a kahler metric of constant scalar curvature the main result of the paper goes some way towards verifying this conjecture in the case of toric surfaces we prove that under the stability hypothesis the mabuchi functional is bounded below on invariant metrics and that minimising sequences have a certain convergence property in the reverse direction we give new examples of polarised surfaces which do not admit metrics of constant scalar curvature the proofs use a general framework developed by guillemin and abreu in which invariant kahler metrics correspond to convex functions on the moment polytope of a toric variety this paper is a step towards the solution of the general problem of finding conditions under which a complex projective variety admits a kahler metric of constant scalar curvature the pattern of the answer one expects is that this differential geometric condition should be equivalent to some notion of stability in the sense of geometric invariant theory this expectation is probably now an item of folklore going back to suggestions put forward by yau in the case of kahlereinstein metrics and the many results of tian and others in this case reinforced by a detailed formal picture which makes clear the analogy with the well established relation between the stability of vector bundles and yang mills connections 5 here we begin the investigation of

mixing heat bath and glauber dynamics damage spreading in the ising model the authors study damage spreading in the ising model on a square lattice by a monte carlo approach using a general f dynamics 0 or f or 1 which reproduces for f 0 the well known heat bath dynamics and for f 1 glauber dynamics they find for initially small damage a critical value fc 0 50 or 0 03 as the threshold for damage spreading for fc f or 1 the damage is non zero only for tc t t0 f where tc is the usual critical temperature and t0 f rises with f like t0 f tc infinity f fc alpha alpha 0 83 or 0 08 for tc or t the damage d t f seems to satisfy the scaling relation d t f approximately mod 1n f fc mod 1t 1 tc t f fc alpha

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

the kahler ricci flow on fano bundles we study the behavior of the kahler ricci flow on some fano bundles which is a trivial bundle on one zariski open set we show that if the fiber is mathbb p m blown up at one point or some weighted projective space blown up at the orbifold point and the initial metric is in a suitable kahler class then the fibers collapse in finite time and the metrics converge sub sequentially in gromov hausdorff sense to a metric on the base

kahler ricci solitons on toric manifolds with positive first chern class abstract in this paper we prove there exists a kahler ricci soliton unique up to holomorphic automorphisms on any toric kahler manifold with positive first chern class and the kahler ricci soliton is a kahler einstein metric if and only if the futaki invariant vanishes

the kahler ricci flow with positive bisectional curvature we show that the kahler ricci flow on a manifold with positive first chern class converges to a kahler einstein metric assuming positive bisectional curvature and certain stability conditions

correlation analysis of the damage spreading problem in a 2 dimensional ising model abstract we have studied the time dependence of the damage spreading in a 2 dimensional ising model using time series analysis we have found that the signal has a hurst exponent 0 5 in high temperatures and it approaches 1 near the temperature t d where the damage goes to zero we have also measured the correlation of the signal and found that it is strongly correlated near t d and describes a persistent fractional brownian motion fbm therefore the hamming distance in the ising model can be used to generate fbm near t d we suggest that the system presents a 1 f spectrum in the transition temperature t d

the kahler ricci flow and k polystability we consider the k ahler ricci flow on a fano manifold we show that if the curvature remains uniformly bounded along the flow the mabuchi energy is bounded below and the manifold is k polystable then the manifold admits a k ahler einstein metric the main ingredient is a result that says that a sufficiently small perturbation of a csck manifold admits a csck metric if it is k polystable

kahler ricci flow on blowups along submanifolds in this short note we study the behavior of kahler ricci flow on kahler manifolds which contract divisors to smooth submanifolds we show that the kahler potentials are holder continuous and the flow converges sequentially in gromov hausdorff topology to a compact metric space which is homeomorphic to the base manifold

convergence of kahler ricci flow in this paper we prove a theorem on convergence of kahler ricci flow on a compact kahler manifold which admits a kahler ricci soliton

space of ricci flows i based on the compactness of the moduli of non collapsed calabi yau spaces with mild singularities we set up a structure theory for polarized kahler ricci flows with proper geo metric bounds our theory is a generalization of the structure theory of non collapsed kahler einstein manifolds as applications we prove the hamilton tian conjecture and the partial c 0 conjecture of tian

the kahler ricci flow on surfaces of positive kodaira dimension 4 estimates 9 4 1 the zeroth order and volume estimates 9 4 2 a partial second order estimate 13 4 3 gradient estimates 14 4 4 the second order estimates 18

kahler ricci flow with degenerate initial class in the earlier joint work 3 we introduced the weak kahler ricci flow for various geometric motivations in this current work we take further consideration on setting up the weak flow by allowing the initial class to be not necessary kahler it s shown that the construction is compatible with the earlier construction in kahler case we also discuss the convergence as t 0 which is of great interest in this topic and provide related motivation 1 motivation and set up of weak flow the kahler ricci flow the complex version of ricci flow has been under intensive study over the last twenty some years in 18 and more recently 17 g tian proposed the intriguing program of constructing globally existing weak kahlerricci flow with canonical singular limit at time infinity and applying it to the study of algebraic manifolds and even kahler manifolds in general it can be viewed as the analytic version of the famous minimal model program in algebraic geometry in general people should expect the classic smooth kahler ricci flow to encounter singularity at some finite time which is completely decided by cohomology information according to the optimal existence result in 20 just as what people have been doing and had successes in cases for ricci flow surgeries for the underlying manifold should be expected for the kahler ricci flow we naturally expect the surgery to have flavours from algebraic geometry a simple example would be surfaces of general type one only needs the blowingdown of 1 curves when applying the general construction at the end of 3 to push the flow through the finite time of singularities where the measure restriction is actually not so involved as explained later in example 4 4 the degenerate class at the singularity time would become kahler for the new manifold because those 1 curves causing the cohomology degeneration would eventually been crushed to points things can get significantly more complicated for higher dimension for example a standard procedure called flip is introduced in the algebraic geometry context which is of great importance for the business about the algebraic minimal model program simply speaking one needs to blow up the manifold and then perform a different blowing down process naturally we should expect the transformation of the degenerate class is still not kahler in this note we confirm that this is not a problem under the assumption that formally the kahler ricci flow is instantly date received on january 6 2012 and accepted on august 22 2012 2010 mathematics subject classification primary 53c44 secondary 14e30 58j35

kahler einstein metrics with positive scalar curvature in this paper we prove that the existence of kahler einstein metrics implies the stability of the underlying kahler manifold in a suitable sense in particular this disproves a long standing conjecture that a compact kahler manifold admits kahler einstein metrics if it has positive first chern class and no nontrivial holomorphic vector fields we will also establish an analytic criterion for the existence of kahler einstein metrics our arguments also yield that the analytic criterion is satisfied on stable kahler manifolds provided that the partial c 0 estimate posed in t6 is true

contracting exceptional divisors by the kahler ricci flow we give a criterion under which a solution g t of the kahler ricci flow contracts exceptional divisors on a compact manifold and can be uniquely continued on a new manifold as t tends to the singular time t from each direction we prove the convergence of g t in the sense of gromov hausdorff and smooth convergence away from the exceptional divisors we call this behavior for the kahler ricci flow a canonical surgical contraction in particular our results show that the kahler ricci flow on a projective algebraic surface will perform a sequence of canonical surgical contractions until in finite time either the minimal model is obtained or the volume of the manifold tends to zero

scalar v soliton equation and kahler ricci flow on symplectic quotients abstract in this paper we consider the v soliton equation which is a degenerate fully nonlinear equation introduced by la nave and tian in their work on kahler ricci flow on symplectic quotients one can apply the interpretation to study finite time singularities of the kahler ricci flow as in the case of kahler einstein metrics we can also reduce the v soliton equation to a scalar equation on kahler potentials which is of monge ampere type we formulate some preliminary estimates for such a scalar equation on a compact kahler manifold m

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends