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arXiv · 2607.10107

Spectral Estimates over Multiply Connected Domains

Georgios Tsikalas
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Abstract

We consider the quantum analogue of a disk with $n$ pairwise disjoint circular holes. We establish a uniform upper bound for the associated spectral constant that is independent of the geometry of the holes, together with a sharper asymptotic bound when the holes are well-separated. The latter generalizes recent estimates for the quantum annulus due to Crouzeix and Pascoe.

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Georgios Tsikalas. 2026-07-11. Spectral Estimates over Multiply Connected Domains. https://arxiv.org/abs/2607.10107

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