相关论文: Visibility in the Boolean Model on Harmonic Manifo…

A closed connected hyperbolic $n$-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic $(n+1)$-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many…

Consider a holomorphic automorphism which acts hyperbolically on some invariant compact set. Then for every point in the compact set there exists a stable manifold, which is a complex manifold diffeomorphic to real Euclidean space. If the…

Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, some new results for the volume of a metric ball in unitary group are derived via various tools from random matrix…

This work presents a reformulation of the recently proposed Wasserstein autoencoder framework on a non-Euclidean manifold, the Poincar\'e ball model of the hyperbolic space. By assuming the latent space to be hyperbolic, we can use its…

In this note, we extend the Bridgeman-Kahn identity to all finite-volume orientable hyperbolic $n$-manifolds with totally geodesic boundary. In the compact case, Bridgeman and Kahn are able to express the manifold's volume as the sum of a…

Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.

We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We…

We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and…

A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as…

Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…

Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general…

We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…

We investigate the behavior of an array of Bose-Einstein condensate tubes described by means of a Bose-Hubbard Hamiltonian. Using an anisotropic non-polynomial Schrodinger equation we link the macroscopic parameters in the Bose-Hubbard…

We experimentally and numerically investigate the expansion of initially localized ultracold bosons in homogeneous one- and two-dimensional optical lattices. We find that both dimensionality and interaction strength crucially influence…

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean…

In this paper we prove a characterization of $p$-hyperbolic ends on complete Riemannian manifolds which carries a Sobolev type inequality.

Let N be a compact, orientable hyperbolic 3-manifold with connected, totally geodesic boundary of genus 2. If N has Heegaard genus at least 5, then its volume is greater than 6.89. The proof of this result uses the following dichotomy:…

Geometric representation learning has recently shown great promise in several machine learning settings, ranging from relational learning to language processing and generative models. In this work, we consider the problem of performing…

Motivated by the computation of loop space quantum mechanics as indicated in [7], here we seek a better understanding of the tubular geometry of loop space ${\cal L}{\cal M}$ corresponding to a Riemannian manifold ${\cal M}$ around the…

Topology describes global quantities invariant under continuous deformations, such as the number of elementary excitations at a phase boundary, without detailing specifics. Conversely, differential laws are needed to understand the physical…