Estimates of the first Dirichlet eigenvalue from exit time moment spectra

A. Hurtado, Steen Markvorsen, V. Palmer

Research output: Contribution to journalJournal articleResearchpeer-review


We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. As an application of the model space theory we prove lower and upper bounds for the first Dirichlet eigenvalues of extrinsic metric balls in submanifolds of ambient Riemannian spaces which have model space controlled curvatures. Moreover, from this general setting we thereby obtain new generalizations of the classical and celebrated results due to McKean and Cheung–Leung concerning the fundamental tones of Cartan-Hadamard manifolds and the fundamental tones of submanifolds with bounded mean curvature in hyperbolic spaces, respectively.
Original languageEnglish
JournalMathematische Annalen
Issue number3
Pages (from-to)1603-1632
Publication statusPublished - 2016


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