An elementary counterexample to Escobar's Steklov conjecture on the three-ball
Alexandre Girouard, Thomas Hélière
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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