Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations

Marco Carfagnini; Maria Gordina; Alexander Teplyaev

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arXiv · 2409.07425

Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations

Marco Carfagnini·Maria Gordina·Alexander Teplyaev

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Abstract

We show that for ultracontractive irreducible Dirichlet metric measure spaces, the Dirichlet spectrum is discrete for a restriction to any connected open set without any assumption on regularity of the boundary. The main applications include small deviations for the corresponding Hunt process and large time asymptotics for the generalized heat content. Our examples include Riemannian and sub-Riemannian manifolds, as well as non-smooth and fractal spaces.

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Marco Carfagnini, Maria Gordina, Alexander Teplyaev. 2024-09-11. Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations. https://arxiv.org/abs/2409.07425

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