The Steklov Spectrum of Convex Polygonal Domains I: spectral finiteness

Authors

Emily DrydenFollow
Carolyn S. Gordon, Dartmouth CollegeFollow
Javier Moreno, Universidad de Los Andes - ColombiaFollow
Julie Rowlett, Chalmers University of TechnologyFollow
Carlos Villegas-Blas, Universidad Nacional Autonoma de MexicoFollow

Publication Date

1-6-2025

Description

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.

Journal

The Journal of Geometric Analysis

Volume

35

Department

Mathematics

Open Access

Link to OA full text

Link to Published Version

https://link.springer.com/article/10.1007/s12220-025-01922-8

DOI

10.1007/s12220-025-01922-8

Recommended Citation

Dryden, Emily; Gordon, Carolyn S.; Moreno, Javier; Rowlett, Julie; and Villegas-Blas, Carlos. "The Steklov Spectrum of Convex Polygonal Domains I: spectral finiteness." (2025) .