A counterexample to quasiconcavity for the Gaussian $p$-Capacity potentials in convex rings

Lei Qin

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arXiv · 2609.14194

A counterexample to quasiconcavity for the Gaussian $p$-Capacity potentials in convex rings

Lei Qin

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Abstract

We construct a smooth, strictly convex ring that admit a unique solution of Gaussian $p$-Capacity problem whose super-level sets are nonconvex. This result provide a negative answer.

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Lei Qin. 2026-09-12. A counterexample to quasiconcavity for the Gaussian $p$-Capacity potentials in convex rings. https://arxiv.org/abs/2609.14194

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