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arXiv · 2609.21877

A Gage-type estimate for the $p$-fundamental tone and applications to submanifolds

Matheus Nunes Soares·Fábio reis dos Santos
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Abstract

A generalization of the classical Gage's upper bound for the fundamental tone of the Laplacian on complete non-compact Riemannian manifolds to the $p$-Laplacian context is obtained. As an application, upper estimates for the $p$-fundamental tone of complete non-compact submanifolds of space forms with constant nonpositive sectional curvature, and for a class of product spaces, are presented.

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Matheus Nunes Soares, Fábio reis dos Santos. 2026-09-18. A Gage-type estimate for the $p$-fundamental tone and applications to submanifolds. https://arxiv.org/abs/2609.21877

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