A note on hot-spots free subregions of convex domains
Abstract
Abstract The second eigenfunction of the Neumann Laplacian on convex, planar domains is considered. Inspired by the famous hot spots conjecture and a related result of Steinerberger, we show that potential critical points of this eigenfunction (and, in particular, interior “hot spots”) cannot be located “near the center” of the domain. The region in which critical points are excluded is described explicitly.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Complex Analysis and Operator Theory
- Volume
- 20
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN