Related papers: Coarse-grained curvature tensor on polygonal surfa…

We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

This paper introduces a novel theoretical framework for identifying Lagrangian Coherent Structures (LCS) in manifolds with non-constant curvature, extending the theory to Finsler manifolds. By leveraging Riemannian and Finsler geometry, we…

In the literature various notions of nonlocal curvature can be found. Here we propose a notion of nonlocal curvature tensor. This we do by generalizing an appropriate representation of the classical curvature tensor and by exploiting some…

We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is…

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…

One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…

We algebraically compute all possible sectional curvature values for canonical algebraic curvature tensors, and use this result to give a method for constructing general sectional curvature bounds. We use a well-known method to…

We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…

The problem of defining correctly geometric objects such as the curvature is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs.…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity…

Solving a long-standing open question in convex geometry, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, we use an easy curvature definition imitating the idea of…

In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…

Minkowski tensors, also known as tensor valuations, provide robust $n$-point information for a wide range of random spatial structures. Local estimators for point clouds, e.g., representing voxelized data, however, are unavoidably biased…

Let R be an algebraic curvature tensor for a non-degenerate inner product of signature(p,q) where q>4. If $\pi$ is a spacelike 2 plane, let $R(\pi)$ be the associated skew-symmetric curvature operator. We classify the algebraic curvature…

This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by…

The tensorial curvature measures are tensor-valued generalizations of the curvature measures of convex bodies. We prove a set of Crofton formulae for such tensorial curvature measures. These formulae express the integral mean of the…

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…