Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 369-01. Strict hot spots and absence of interior critical points on smooth simply connected planar domains
Manuscript map · lines 9465–9474
OpenAI@2026-10-07#rem:oai-p-369-01
Authors: OpenAI. Family 369.
Title: Strict hot spots and absence of interior critical points on smooth simply connected planar domains.
Abstract: We prove the strict hot spots conjecture for smooth bounded simply connected planar domains. More precisely, every nonzero eigenfunction for the first positive Neumann eigenvalue has nonvanishing gradient in the interior, so all its global maxima and minima lie on the boundary. This holds even when the eigenvalue is multiple.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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