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Strict hot spots on simply connected planar domains

The strict version concerns every eigenfunction, rather than existence of one favorable eigenfunction or results confined to convex or symmetric domains.

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Understanding the problem

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The strict version concerns every eigenfunction, rather than existence of one favorable eigenfunction or results confined to convex or symmetric domains.

The domain is smooth, bounded, and simply connected. No assertion for domains with holes or arbitrary boundary regularity is recorded.

Why it matters

If correct, establishes the stated strict all-eigenfunction hot-spots target without convexity or symmetry restrictions.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The domain is smooth, bounded, and simply connected. No assertion for domains with holes or arbitrary boundary regularity is recorded.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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