Related papers: On systoles and ortho spectrum rigidity

We construct a family of hyperbolic string vertices in the oriented open-closed string field theory, generalizing the recent result on hyperbolic closed string vertices by Costello and Zwiebach. The vertices are described by certain…

Let $M$ be a $2m$-dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on $m$-forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics.…

Inspired by [6, 7], we study the boundary regularity of constant curvature hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$, which have prescribed asymptotic boundary at infinity. Through constructing the boundary expansions of the…

We give a proof of an unpublished result of Thurston showing that given any hyperbolic metric on a surface of finite type with nonempty boundary, there exists another hyperbolic metric on the same surface for which the lengths of all simple…

We consider a coarse version of the marked length spectrum rigidity: given a group with two left invariant metrics, if the marked length spectrum (the translation length function) under the two metrics are the same, then the two metrics are…

This article presents some methods to control the bottom of the spectrum of the Laplacian $\lambda_0$ on hyperbolic surfaces with infinite volume. Our first result bounds the $\lambda_0$ of a geometrically finite surface in terms of the…

We compute the number of systoles, the shortest simple closed geodesics and 2-systoles, the second shortest simple closed geodesics on hyperbolic surfaces homeomorphic to once-punctured torus and four-punctured sphere.

Given a group $G$ acting geometrically on a systolic complex $X$ and a hyperbolic isometry $h \in G$, we study the associated action of $h$ on the systolic boundary $\partial X$. We show that $h$ has a canonical pair of fixed points on the…

We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive $\delta'$ interaction supported by a smooth surface in $\R^3$, either infinite and asymptotically planar, or compact and closed. Its second term is…

In this paper we examine the geometry of minimal surfaces of arithmetic hyperbolic 3-manifolds. In particular, we give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial…

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…

We identify a condition that prevents a hyperbolic space from being quasi-isometric to the curve complex of any non-sporadic surface. Our result applies to several hyperbolic complexes, including arc complexes, disk complexes,…

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the…

We consider the asymptotic behavior of properly embedded minimal surfaces in the product of the hyperbolic plane with the line, taking into account the fact that there is more than one natural compactification of this space. This provides a…

We propose a general framework for studying pseudo-Anosov homeomorphisms on translation surfaces. This new approach, among other consequences, allows us to compute the systole of the Teichmueller geodesic flow restricted to the…

We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.

For a closed and orientable surface of genus at least 2, we prove the surface group extensions of the stabilizers of multicurves are hierarchically hyperbolic groups. This answers a question of Durham, Dowdall, Leininger, and Sisto. We also…

Our main result is that for all sufficiently large $x_0>0$, the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field $k$ and systole bounded below by $x_0$ has density one within the…

We consider a closed negatively curved surface $(M, g)$ with marked length spectrum sufficiently close (multiplicatively) to that of a hyperbolic metric $g_0$ on $M$. We show there is a smooth diffeomorphism $F:M \to M$ with derivative…

We study the systole of a random surface, where by a random surface we mean a surface constructed by randomly gluing together an even number of triangles. We study two types of metrics on these surfaces, the first one coming from using…