Related papers: Bridgeman's orthospectrum identity
We present an orthogonal basis for functions over a slice of the Boolean hypercube. Our basis is also an orthogonal basis of eigenvectors for the Johnson and Kneser graphs. As an application of our basis, we streamline Wimmer's proof of…
We give a description of ergodic components of SRB measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points. For transitive surface diffeomorphisms, we prove that there exists at most one SRB measure.
We study closed geodesics on hyperbolic surfaces, and give bounds for their angles of intersection and self-intersection, and for the sides of the polygons that they form, depending only on the lengths of the geodesics
We consider various equivalence relations on the set of homotopy classes of curves on a hyperbolic surface based on topological, algebraic, and geometric structures. The purpose of this work is to determine the relationship between these…
Using recent work of Bourgain-Dyatlov we show that for any convex co-compact hyperbolic surface Strichartz estimates for the Schr\"odinger equation hold with an arbitrarily small loss of regularity.
We define Bregman variation of semimartingales. We give its pathwise representation, It\^o-type isometry for martingales, and applications to harmonic analysis.
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
In this paper we study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods…
Volume is a natural measure of complexity of a Riemannian manifold. In this survey, we discuss the results and conjectures concerning n-dimensional hyperbolic manifolds and orbifolds of small volume.
We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower…
This note is about the spectral properties of transfer operators associated to smooth hyperbolic dynamics. In the first two sections (written in 2006), we state our new results relating such spectra with dynamical determinants, first…
We reveal the existence of a new type of surface electromagnetic waves supported by hyperbolic metasurfaces, described by a conductivity tensor with an indefinite signature. We demonstrate that the spectrum of the hyperbolic metasurface…
We prove an isoperimetric inequalitie on the complex hyperbolic ball with Assumption \ref{assumption}}. As an application, we prove a contraction property for the holomorphic functions in Hardy and weighted Bergman spaces on the complex…
We define a new notion of translations in the hyperbolic plane and explicitly solve the equation of the curve shortening flow. Next, we consider the class of ancient convex solutions and solve the equation of the curve shortening flow when…
We study the Kobayashi pseudodistance for orbifolds, proving an orbifold version of Brody's theorem and classifying which one-dimensional orbifolds are hyperbolic.
We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in terms of the series involving hyperbolic functions, digamma function, Bernoulli numbers etc. In this version, inaccuracies…
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal…
We study the growth of hyperbolic type distances in starlike domains. We derive estimates for various hyperbolic type distances and consider the asymptotic sharpness of the estimates.
We show that in the absence of periodic centre annuli, a partially hyperbolic surface endomorphism is dynamically coherent and leaf conjugate to its linearisation. We proceed to characterise the dynamics in the presence of periodic centre…
We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by…