The second Robin eigenvalue in non-compact rank-1 symmetric spaces
Differential Geometry
2022-08-17 v1 Analysis of PDEs
Spectral Theory
Abstract
In this paper, we prove a quantitative spectral inequality for the second Robin eigenvalue in non-compact rank-1 symmetric spaces. In particular, this shows that for bounded domains in non-compact rank-1 symmetric spaces, the geodesic ball maximises the second Robin eigenvalue among domains of the same volume, with negative Robin parameter in the regime connecting the first nontrivial Neumann and Steklov eigenvalues. This result generalises the work of Freitas and Laugesen in the Euclidean setting [FL21] as well as our previous work in the hyperbolic space [LWW20].
Keywords
Cite
@article{arxiv.2208.07546,
title = {The second Robin eigenvalue in non-compact rank-1 symmetric spaces},
author = {Xiaolong Li and Kui Wang and Haotian Wu},
journal= {arXiv preprint arXiv:2208.07546},
year = {2022}
}
Comments
16 pages. Comments are welcome. arXiv admin note: substantial text overlap with arXiv:2003.03087