Monotonicity results for the first Steklov eigenvalue on compact surfaces
arXiv:1801.08518
Abstract
We show several results comparing sharp eigenvalue bounds for the first Steklov eigenvalue on surfaces under change of the topology. Among others, we obtain strict monotonicity in the genus. Combined with results of the second named author \cite{petrides_2} this implies the existence of free boundary minimal immersions from higher genus surfaces into Euclidean balls. Moreover, we can also give a new proof of a result by Fraser and Schoen that shows monotonicity in the number of boundary components.
arXiv commentsuperseded by arXiv:2004.06051
References in corpus (6)
- Regularity of Solutions of Linear Second Order Elliptic and Parabolic Boundary Value Problems on Lipschitz Domains
- Free boundary minimal surfaces of unbounded genus
- Free Boundary Minimal Surfaces in the Unit Three-Ball via Desingularization of the Critical Catenoid and the Equatorial Disk
- Equivariant min-max theory
- Maximal metrics for the first Steklov eigenvalue on surfaces
- Spectral geometry of the Steklov problem