Related papers: Isosystolic inequalities for optical hypersurfaces

It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of $\mathbb{R}^n$. In the $3$-dimensional case…

The theory of intrinsic volumes of convex cones has recently found striking applications in areas such as convex optimization and compressive sensing. This article provides a self-contained account of the combinatorial theory of intrinsic…

The extreme anisotropy of hyperbolic materials enables extreme wave confinement, but it is also associated with an inherent misalignment between phase and energy flow, which complicates device modeling and design. Here we introduce a…

A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a…

In 1978, Makai Jr. established a remarkable connection between the volume-product of a convex body, its maximal lattice packing density and the minimal density of a lattice arrangement of its polar body intersecting every affine hyperplane.…

We develop a min-max theory for certain complete minimal hypersurfaces in hyperbolic space. In particular, we show that given two strictly stable minimal hypersurfaces that are both asymptotic to the same ideal boundary, there is a new one…

The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be…

We first prove that given a hyperbolic metric $h$ on a closed surface $S$, any flat metric on $S$ with negative singular curvatures isometrically embeds as a convex polyhedral Cauchy surface in a unique future-complete flat globally…

In this note we study the systoles of convex hypersurfaces in $\mathbb{R}^{2n}$ invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the…

We use the intrinsic area to define a distance on the space of homothety classes of convex bodies in the $n$-dimensional Euclidean space, which makes it isometric to a convex subset of the infinite dimensional hyperbolic space. The ambient…

We construct pairs of non-isometric hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic)…

In this article we introduce a hyperbolic metric on the (normalized) space of stability conditions on projective K3 surfaces $X$ with Picard rank $\rho (X) =1$. And we show that all walls are geodesic in the normalized space with respect to…

We prove three facts about intrinsic geometry of surfaces in a normed (Minkowski) space. When put together, these facts demonstrate a rather intriguing picture. We show that (1) geodesics on saddle surfaces (in a space of any dimension)…

We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of…

Let F be a surface and suppose that \phi: F -> F is a pseudo-Anosov homeomorphism fixing a puncture p of F. The mapping torus M = M_\phi is hyperbolic and contains a maximal cusp C about the puncture p. We show that the area (and height) of…

We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…

We fully characterize the set of finite shapes with minimal perimeter on hyperbolic lattices given by regular tilings of the hyperbolic plane whose tiles are regular $p$-gons meeting at vertices of degree $q$, with $1/p+1/q<\frac{1}{2}$. In…

We generalize the Hyperbolic Fracton Model from the $\{5,4\}$ tessellation to generic tessellations, and investigate its core properties: subsystem symmetries, fracton mobility, and holographic correspondence. While the model on the…

We prove that a 3-dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by the metric induced on its boundary. Furthemore, any hyperbolic metric on the torus with cone singularities of positive curvature can be…

Using a navigation process with the datum $(F,V)$, in which $F$ is a Finsler metric and the smooth tangent vector field $V$ satisfies $F(-V(x))>1$ everywhere, a Lorentz Finsler metric $\tilde{F}$ can be induced. Isoparametric functions and…