On the second Robin eigenvalue of the Laplacian
Differential Geometry
2020-03-09 v1 Analysis of PDEs
Spectral Theory
Abstract
We study the Robin eigenvalue problem for the Laplace-Beltrami operator on Riemannian manifolds. Our first result is a comparison theorem for the second Robin eigenvalue on geodesic balls in manifolds whose sectional curvatures are bounded from above. Our second result asserts that geodesic balls in nonpositively curved space forms maximize the second Robin eigenvalue among bounded domains of the same volume.
Cite
@article{arxiv.2003.03087,
title = {On the second Robin eigenvalue of the Laplacian},
author = {Xiaolong Li and Kui Wang and Haotian Wu},
journal= {arXiv preprint arXiv:2003.03087},
year = {2020}
}
Comments
Comments are welcome