PreprintarXiv licencearXiv
A counterexample to quasiconcavity for the Gaussian p-Capacity potentials in convex rings
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.
Related
- A Counterexample to a Problem of Pommerenke on Convex Functions in the Class Σ
- Counterexample to a Proposed Capacity Characterization of the Relay Channel
- Observability of wave equations with time- and space-dependent potentials: a counterexample under GCC and a positive criterion on the disk
- Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentials
- Stochastic Subgradient Descent at Sharply Repulsive Points: A Bounded Noise Counterexample and Gaussian Noise Avoidance
BibTeX
@misc{qin2026counterexample,
title = {{A counterexample to quasiconcavity for the Gaussian $p$-Capacity potentials in convex rings}},
author = {Lei Qin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14194},
eprint = {2609.14194},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14194},
}
RIS
TY - UNPB
TI - A counterexample to quasiconcavity for the Gaussian p-Capacity potentials in convex rings
AU - Lei Qin
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.14194
UR - https://arxiv.org/abs/2609.14194
AB - 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.
ER -