相关论文: Vector-valued horofunction boundaries and Patterso…

Two commonly studied compactifications of Teichm\"uller spaces of finite type surfaces with respect to the Teichm\"uller metric are the horofunction and visual compactifications. We show that these two compactifications are related, by…

This paper develops a theory of conformal density at infinity for groups with contracting elements. We start by introducing a class of convergence boundary encompassing many known hyperbolic-like boundaries, on which a detailed study of…

Our monograph presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Our work unifies and extends a long list of results by many authors. We make it a point to avoid any…

In this paper we answer positively a question raised by Kapovich and Leeb in a paper titled "Finsler bordifications of symmetric and certain locally symmetric spaces". Specifically, we show that for a finite-dimensional vector space with a…

We establish (some directions) of a Ledrappier correspondence between H\"older cocycles, Patterson-Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow. We then study Patterson-Sullivan measures for…

It is suggested a testing puzzle able to reveal the self-asserting property of the homogeneous vector potential field. As pieces of the puzzle are taken three reliable entities : (i) influence of a potential vector on the de Broglie…

For any rank-one convex projective manifold with a compact convex core, we prove that there exists a unique probability measure of maximal entropy on the set of unit tangent vectors whose geodesic is contained in the convex core, and that…

We show that a relatively ergodic extension of measure-preserving dynamical systems has relative discrete spectrum if and only if it can be represented as a skew-product by a bundle of compact homogeneous spaces. Our result holds without…

An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed…

We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but…

We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly…

This article is a survey of recent work of the author, together with Markus Banagl, Eric Leichtnam, Rafe Mazzeo, and Paolo Piazza, on the Hodge theory of stratified spaces. We discuss how to resolve a Thom-Mather stratified space to a…

We consider horofunction compactifications of symmetric spaces with respect to invariant Finsler metrics. We show that any (generalized) Satake compactification can be realized as a horofunction compactification with respect to a polyhedral…

Let $\Gamma$ be some discrete subgroup of $\mathbf{SO}^o(n+1,\mathbf{R})$ with finite Bowen-Margulis-Sullivan measure. We study the dynamics of the Bowen-Margulis-Sullivan measure with respect to closed connected subspaces of the $N$…

With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities)…

We apply a theorem of Gel'fand, Goresky, MacPherson, and Serganova about matroid polytopes to study semistability of partial flags relative to a T-linearized ample line bundle of a flag space F = SL(n)/P where T is a maximal torus in SL(n)…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

If $M$ is a compact or convex-cocompact negatively curved manifold, we associate to any Gibbs measure on $\tm$ a quasi-invariant transverse measure for the horospherical foliation, and prove that this measure is uniquely determined by its…

Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which…

In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.