A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions

2025/01/07 by Gabriel Khan, Khan, Gabriel, Soumyajit Saha +3
Computer Science · Mathematics · #58J50 35B45 35B50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2501.03504

openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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