The first Steklov eigenvalue of graphs of positive genus
Abstract
Abstract Let be a graph of genus with boundary . For , Lin and Zhao [J. Lond. Math. Soc. 112 (2025), Paper No. e70238] proved an upper bound for the first (non‐trivial) Steklov eigenvalue of , and they posed the problem of determining a corresponding bound for graphs of genus . In this paper, we prove an bound for a bounded‐degree graph of positive genus . Our result can be regarded as a discrete analogue of Kokarev's bound [Adv. Math. 258 (2014), 191–239], up to a constant factor.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 3
- Publication date
- 1 March 2026
- Language
- EN