Related papers: Finiteness of gibbs measures on noncompact manifol…

We prove for $C^\infty$ non-singular flows on three-dimensional compact manifolds with positive entropy, there are at most finitely many ergodic measures of maximal entropy. This result extends the notable work of Buzzi-Crovisier-Sarig…

Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…

One proves the equivalence of a Gibbs measure and a Gibbs conformal measure for a dynamical system (G,X) when G is a countably infinite discrete group acting expansively on a compact ultrametric space X. As an application one proves for any…

We study a broad class of local homeomorphisms and continuous potentials, proving the existence and uniqueness of weak Gibbs measures. From the Gibbs property, we show the uniqueness of equilibrium states and derive a large deviations…

In this work, we provide two novel approaches to show that incompressible fluid flow in a finite domain contains at most a finite number vortices. We use a recently developed geometric theory of incompressible viscous flows along with an…

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of…

We study when Fourier transforms of Gibbs measures of sufficiently nonlinear expanding Markov maps decay at infinity at a polynomial rate. Assuming finite Lyapunov exponent, we reduce this to a nonlinearity assumption, which we verify for…

In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be…

Consider the radial nonlinear wave equation $-\partial_t^2 u + \Delta u = u^3$, $u :\mathbb{R}_t \times \mathbb{R}_x^3 \to \mathbb{R}$, $u(t,x) = u(t,|x|)$. In this paper, we construct a Gibbs measure for this system and prove its…

We study the Hausdorff dimension of Gibbs measures with infinite entropy with respect to maps of the interval with countably many branches. We show that under simple conditions, such measures are symbolic-exact dimensional, and provide an…

We study the generic invariant probability measures for the geodesic flow on connected complete nonpositively curved manifolds. Under a mild technical assumption, we prove that ergodicity is a generic property in the set of probability…

It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct…

For a large class of irreducible shift spaces $X\subset\tA^{\Z^d}$, with $\tA$ a finite alphabet, and for absolutely summable potentials $\Phi$, we prove that equilibrium measures for $\Phi$ are weak Gibbs measures. In particular, for…

We show that in a rapidly mixing flow with an invariant measure, the time which is needed to hit a given section is related to a sort of conditional dimension of the measure at the section. The result is applied to the geodesic flow of…

In a previous paper the authors developed a H^1-BMO theory for unbounded metric measure spaces $(M,\rho,m)$ of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and…

We construct infinitely many examples of finite volume 4-manifolds with $T^3$ ends that do not admit any cusped asymptotically hyperbolic Einstein metrics yet satisfy a strict logarithmic version of the Hitchin-Thorpe inequality due to…

In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cellular decompositions. To address this problem, we introduce…

We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be irreversible but should satisfy some mild…

We consider the one dimensional cubic nonlinear Schr{\"o}dinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to the equation and prove that the Cauchy problem is globally…

In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide…