PDE and mathematical physics · Aug 5, 2026
Planar Schiffer / Pompeiu rigidity
Noncircular counterexamples are reported, including a real-analytic Jordan domain from computer-assisted existence estimates and a separate bifurcation construction.
Scope and what remains
Preserve boundedness, topology, boundary regularity and the nonconstant-eigenfunction requirement; an annulus does not settle the simply connected question. Do not merge two arguments merely because they resolve the same question.
Contributors
Matthew Colbrook and Grigory Stepaniants for one construction; Gonzalo Cao-Labora and Jaume de Dios Pont for another. AI-assisted proof/formalization attribution must remain artifact-specific.
AI systems: GPT-5.6, Claude Opus 4.8, Claude Fable 5