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arXiv · 2412.20281

Nonlinear potential theory and Ricci-pinched 3-manifolds

Luca Benatti·Ariadna León Quirós·Francesca Oronzio·Alessandra Pluda
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Abstract

In this paper, we focus on Hamilton's pinching conjecture formulated in Hamilton's paper "Three-manifolds with positive Ricci curvature". Let $(M, g)$ be a complete, connected, noncompact Riemannian $3$-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.

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Luca Benatti, Ariadna León Quirós, Francesca Oronzio, Alessandra Pluda. 2024-12-28. Nonlinear potential theory and Ricci-pinched 3-manifolds. https://arxiv.org/abs/2412.20281

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