Maximizers Beyond the Hemisphere for the Second Neumann Eigenvalue

Authors

Jeffrey J. Langford, Bucknell UniversityFollow
Richard Laugesen, University of Illinois at Urbana-Champaign

Publication Date

2023

Description

The first positive Neumann eigenvalue of the Laplacian is shown to be maximal for a spherical cap among simply connected domains covering up to 94% of the 2-sphere. The previous best result, by Bandle, was 50%.

Journal

Mathematische Annalen

Volume

386

Issue

3-4

First Page

2255

Last Page

2281

Department

Mathematics

Link to Published Version

https://link.springer.com/article/10.1007/s00208-022-02455-z

DOI

https://doi.org/10.1007/s00208-022-02455-z

Recommended Citation

Langford, Jeffrey J. and Laugesen, Richard. "Maximizers Beyond the Hemisphere for the Second Neumann Eigenvalue." (2023) : 2255-2281.