Work

A note on hot-spots free subregions of convex domains

Year: 2026

Type: article

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.

Source: Complex Analysis and Operator Theory

DOI: 10.1007/s11785-026-01910-y

Author: Jonathan Rohleder

Institution: Stockholm University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Vetenskapsrådet, Stockholms Universitet