Related papers: Ergodicity of two hard balls in integrable polygon…
The paper concentrates on the application of the following Hardy inequality \begin{equation*} \int_\Omega \ |\xi(x)|^p \omega_{1 }(x)dx\le \int_\Omega |\nabla \xi(x)|^p\omega_{2 }(x)dx, \end{equation*} to the proof of existence of weak…
In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study the weighted boundedness. Motivated in the weighted boundedness of Hardy-Littlewood maximal studied by Antezana…
We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of those polyhedra are hyperbolic buildings, which appartments are hyperbolic planes tesselated by regular triangles with angles $\pi/4$.…
In the seminal work of Balogh-Buckley [Invent. Math. 2003], the authors asked the following fundamental open problem: for proper subdomains in the Euclidean space $\mathbb{R}^n$, does the ball separation condition alone imply the…
In this note, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to $\mathcal{C}^2$-smooth maps on the boundary.
In this note we give several characterisations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…
Recently, strongly hyperbolic space as certain analytic enhancements of Gromov hyperbolic space was introduced by B. Nica and J. Spakula. In this note, we prove that the log-metric log(1+d) on a Ptolemy space (X,d) is a strongly hyperbolic…
A triangulation of a surface is \emph{irreducible} if there is no edge whose contraction produces another triangulation of the surface. We prove that every irreducible triangulation of a surface with Euler genus $g\geq1$ has at most $13g-4$…
We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the…
We study approximation properties of weighted $L^2$-orthogonal projectors onto spaces of polynomials of bounded degree in the Euclidean unit ball, where the weight is of the generalized Gegenbauer form $x \mapsto (1-\|x\|^2)^\alpha$,…
We derive an explicit lower bound on the radius of a ball embedded in a quaternionic hyperbolic manifold.
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering the space variable-independent solutions only. This simplification leads to a degenerate…
We give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any $n>0$, we show that there exists a space of geodesic…
Shift spaces with the specification property are intrinsically ergodic, i.e. they have a unique measure of maximal entropy. This can fail for shifts with the weaker almost specification property. We define a new property called one-sided…
Bernoulli's free boundary problem is an overdetermined problem in which one seeks an annular domain such that the capacitary potential satisfies an extra boundary condition. There exist two different types of solutions called elliptic and…
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…
We present some properties of hyperkahler torsion (or heterotic) geometry in four dimensions that make it even more tractable than its hyperkahler counterpart. We show that in $d=4$ hypercomplex structures and weak torsion hyperkahler…
Kerckhoff and Storm conjectured that compact hyperbolic n-orbifolds with totally geodesic boundary are infinitesimally rigid when n>3. This paper verifies this conjecture for a specific example based on the 4-dimensional hyperbolic…
In [11], employing the technique of noncommutative interpolation, a maximal ergodic theorem in noncommutative Lp-spaces, 1 < p < infinity, was established and, among other things, corresponding maximal ergodic inequalities and individual…
In this paper, we prove a rigidity theorem of asymptotically hyperbolic manifolds only under the assumptions on curvature. Its proof is based on analyzing asymptotic structures of such manifolds at infinity and a volume comparison theorem.