Year: 2026
Type: preprint
Abstract: We give a reduction from a smooth-domain theorem excluding interior critical points of first positive Neumann eigenfunctions to a non-strict hot-spots conclusion on arbitrary bounded simply connected planar domains with compact Neumann resolvent and simple first positive eigenvalue. The main analytic step is spectral convergence under exhaustion by conformal images of concentric disks. A reflection extension, conformal invariance of Dirichlet energy, and compactness of the Sobolev embedding give a direct proof. A truncation argument justifies square integrability of the transferred extensions without any boundary regularity. The smooth-domain theorem proved by OpenAI is an external input; the approximation argument is proved here in full. The paper was generated by ChatGPT with prompts from the listed author.
Source: arXiv (Cornell University)
Author: Burdzy, Krzysztof
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221528670