Nonlinear potential theory and Ricci-pinched 3-manifolds
Differential Geometry
2026-02-11 v3
Abstract
In this paper, we focus on Hamilton's pinching conjecture formulated in Hamilton's paper "Three-manifolds with positive Ricci curvature". Let be a complete, connected, noncompact Riemannian -manifold satisfying the Ricci-pinching condition. Then, it is flat. Here, we give an alternative proof, based on nonlinear potential theory, under the extra hypothesis of superquadratic volume growth.
Cite
@article{arxiv.2412.20281,
title = {Nonlinear potential theory and Ricci-pinched 3-manifolds},
author = {Luca Benatti and Ariadna León Quirós and Francesca Oronzio and Alessandra Pluda},
journal= {arXiv preprint arXiv:2412.20281},
year = {2026}
}