Related papers: Sharp geometric upper bounds on resonances for sur…

This paper is about closed hyperbolic surface amalgams with a focus on the growth of the number of closed geodesics. As in the case of surfaces, we show that topological and volume entropies coincide, but we show stark differences in how…

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic…

Manifolds with infinite cylindrical ends have continuous spectrum of increasing multiplicity as energy grows, and in general embedded resonances (resonances on the real line, embedded in the continuous spectrum) and embedded eigenvalues can…

The spectral radius {\rho}(G) of a digraph G is the maximum modulus of the eigenvalues of its adjacency matrix. We present bounds on {\rho}(G) that are often tighter and are applicable to a larger class of digraphs than previously reported…

In the spirit of Otal and Croke, we prove that a negatively-curved asymptotically hyperbolic surface is boundary distance rigid, where the distance between two points on the boundary at infinity is defined by a renormalized quantity.

In this paper, we investigate the asymptotic behavior of regular ends of flat surfaces in the hyperbolic 3-space H^3. Galvez, Martinez and Milan showed that when the singular set does not accumulate at an end, the end is asymptotic to a…

In the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we show that a geodesically complete hyperbolic surface is made up of its convex…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

The nonlocal order parameter equation for nonlinear optical resonator is approximated in the limit of high Fresnel number by the Swift- Hohenberg equation. The exact soliton and periodic solutions of the Swift- Hohenberg equation for…

We improve the best known upper bounds on the number of Ruelle resonances in disks of large radius for Gevrey uniformly hyperbolic flows. The proof is based on Rugh's approach of dynamical determinants that replaces the study of the flow…

We consider harmonic immersions in $\R^{\N}$ of compact Riemann surfaces with finitely many punctures where the harmonic coordinate functions are given as real parts of meromorphic functions. We prove that such surfaces have finite total…

We study the global behavior of (weakly) stable constant mean curvature hypersurfaces in general Riemannian manifolds. By using harmonic function theory, we prove some one-end theorems which are new even for constant mean curvature…

We prove existence of thick geodesic triangulations of hyperbolic 3-manifolds and use this to prove existence of universal bounds on the principal curvatures of surfaces embedded in hyperbolic 3-manifolds.

We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend…

We consider a magnetic Laplacian on a geometrically finite hyperbolic surface, when the corresponding magnetic field is infinite at the boundary at infinity. We prove that the counting function of the eigenvalues has a particular asymptotic…

We show that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot. This leads to diagrammatic estimates on lengths of slopes, and has some…

We adapt linear programming methods from sphere packings to closed hyperbolic surfaces and obtain new upper bounds on their systole, their kissing number, the first positive eigenvalue of their Laplacian, the multiplicity of their first…

We prove Fourier restriction estimates by means of the polynomial partitioning method for compact subsets of any sufficiently smooth hyperbolic hypersurface in threedimensional euclidean space. Our approach exploits in a crucial way the…

The Epstein-Penner convex hull construction associates to every decorated punctured hyperbolic surface a polyhedral convex body in the Minkowski space. It works in the de Sitter and anti-de Sitter spaces as well. In these three spaces, the…

We study the intrinsic geometry of area minimizing (and also of almost minimizing) hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. For any such hypersurface we define and construct a so-called…