A counterexample to the convexity property of the first eigenfunction on a convex domain of negative curvature

DOI10.1080/03605308908820634zbMath0681.35030OpenAlexW2019968693MaRDI QIDQ4730157

Ying Shih

Publication date: 1989

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308908820634

zbMATH Keywords

Riemannian manifoldlogarithmic convexity

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral theory; eigenvalue problems on manifolds (58C40) Qualitative properties of solutions to partial differential equations (35B99)

Related Items (5)

Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains ⋮ Mini-workshop: A geometric fairytale full of spectral gaps and random fruit. Abstracts from the mini-workshop held November 27 -- December 3, 2022 ⋮ Convexity of level sets of minimal graph on space form with nonnegative curvature ⋮ Stability results for the first eigenvalue of the Laplacian on domains in space forms. ⋮ The vanishing of the fundamental gap of convex domains in \(\mathbb{H}^n\)

Cites Work

• Unnamed Item
• Convex solutions of certain elliptic equations have constant rank Hessians
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem
• Convexity properties of solutions to some classical variational problems

This page was built for publication: A counterexample to the convexity property of the first eigenfunction on a convex domain of negative curvature