An elementary counterexample to Escobar's Steklov conjecture on the three-ball

Alexandre Girouard; Thomas Hélière

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arXiv · 2608.25214

An elementary counterexample to Escobar's Steklov conjecture on the three-ball

Alexandre Girouard·Thomas Hélière

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Abstract

We give an explicit polynomial deformation of the Euclidean metric on the unit three-ball which has positive Ricci curvature and strictly convex boundary but violates Escobar's conjectured lower bound for the first nonzero Steklov eigenvalue. Our proof is fully human-verifiable.

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BibTeX RIS

Alexandre Girouard, Thomas Hélière. 2026-08-25. An elementary counterexample to Escobar's Steklov conjecture on the three-ball. https://arxiv.org/abs/2608.25214

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