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arXiv · 2501.03504

A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions

Gabriel Khan·Soumyajit Saha·Malik Tuerkoen
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Abstract

In this paper, we establish a priori log-concavity estimates for the first Dirichlet eigenfunction of convex domains of a Riemannian manifold. Specifically, we focus on cases where the principal eigenfunction $u$ is assumed to be log-concave and our primary goal is to obtain quantitative estimates for the Hessian of $\log u$.

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Gabriel Khan, Soumyajit Saha, Malik Tuerkoen. 2025-01-07. A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions. https://arxiv.org/abs/2501.03504

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