Work

Sobolev metrics on spaces of discrete regular curves

Year: 2025

Type: article

Abstract: Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and considers the induced Riemannian metric on a finite dimensional approximation space. Surprisingly, the theoretical properties of the corresponding finite dimensional Riemannian manifolds have not yet been studied in detail, which is the content of the present article. Our main theorem concerns metric and geodesic completeness and mirrors the results of the infinite dimensional setting as obtained by Bruveris, Michor and Mumford.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025086

Authors: Jonathan Cerqueira, Emmanuel Hartman, Eric Klassen, Martin Bauer

Institution: Florida State University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Directorate for Computer and Information Science and Engineering

Awards: Collaborative Research: Data-Driven Elastic Shape Analysis with Topological Inconsistencies and Partial Matching Constraints, Collaborative Research: CISE-ANR: RI: Small: 4DShape: 4D Human Shape Analysis and Synthesis, eMB: New Approaches for Interpreting Neural Responses to Behaviorally-Relevant Sensory Stimuli, Collaborative Research: Data-Driven Elastic Shape Analysis with Topological Inconsistencies and Partial Matching Constraints