Year: 2026
Type: preprint
Abstract: We prove that isolated spectral clusters preserve their finite-group representation under equivariant spectral convergence. In particular, an irreducible limiting eigenspace cannot split into several nearby eigenvalues, while an isotypic limiting eigenspace imposes corresponding divisibility constraints on the multiplicities in the approximating cluster. We then construct a one-parameter equivariant Steklov homogenisation on closed orientable surfaces, allowing Laplace spectral representations to be transferred to Steklov spectral clusters. Applied to the hyperbolic surfaces of Fortier Bourque, Gruda-Mediavilla, Petri, and Pineault, this yields first Steklov multiplicities 16 and 21 in genera 10 and 17, and at least 24 in genus 37. These examples give counterexamples to Jammes's conjecture on first Steklov multiplicity.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221532409