Work

The Steklov Spectrum of Convex Polygonal Domains I: Spectral Finiteness

Year: 2025

Type: article

Abstract: We explore the Steklov eigenvalue problem on convex polygons, focusing mainly on the inverse Steklov problem. Our primary finding reveals that, for almost all convex polygonal domains, there exist at most finitely many non-congruent domains with the same Steklov spectrum. Moreover, we obtain explicit upper bounds for the maximum number of mutually Steklov isospectral non-congruent polygonal domains. Along the way, we obtain isoperimetric bounds for the Steklov eigenvalues of a convex polygon in terms of the minimal interior angle of the polygon.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-025-01922-8

Authors: Emily B. Dryden, Carolyn Gordon, Javier Moreno, Julie Rowlett, Carlos Villegas-Blas

Institutions: Bucknell University, Dartmouth College, Universidad de Los Andes, Chalmers University of Technology, Universidad Nacional Autónoma de México

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Chalmers Tekniska Högskola, Consejo Nacional de Ciencia y Tecnología