Nonlinear potential theory and Ricci-pinched 3-manifolds

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.

💡 Research Summary

This paper provides a new proof of Hamilton’s pinching conjecture for three‑dimensional Ricci‑pinched manifolds, using tools from nonlinear potential theory rather than Ricci flow or inverse mean curvature flow. The authors consider a complete, connected, non‑compact Riemannian 3‑manifold ((M,g)) that satisfies the Ricci‑pinching condition
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