正利玛窦曲率的 3 球体中存在 5 个最小转矩

arXiv - MATH - Geometric Topology Pub Date : 2024-09-14 DOI:arxiv-2409.09315

Adrian Chun-Pong Chu, Yangyang Li

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摘要

1989 年，B. 怀特猜想每个黎曼 3 球至少有 5 个嵌入的最小环。我们对具有正里奇曲率的 3 球体证实了这一猜想。虽然我们的证明使用了最小最大理论，但其基本启发式主要来自平均曲率流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Existence of 5 minimal tori in 3-spheres of positive Ricci curvature

In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5 embedded minimal tori. We confirm this conjecture for 3-spheres of positive Ricci curvature. While our proof uses min-max theory, the underlying heuristics are largely inspired by mean curvature flow.

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arXiv - MATH - Geometric Topology

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