Existence of four minimal spheres in $S^3$ with a bumpy metric

Zhichao Wang; Xin Zhou

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arXiv · 2305.08755

Existence of four minimal spheres in $S^3$ with a bumpy metric

Zhichao Wang·Xin Zhou

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Abstract

We prove that in the three dimensional sphere with a bumpy metric or a metric with positive Ricci curvature, there exist at least four distinct embedded minimal two-spheres. This confirms a conjecture of S. T. Yau in 1982 for bumpy metrics and metrics with positive Ricci curvature. The proof relies on a multiplicity one theorem for the Simon-Smith min-max theory.

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BibTeX RIS

Zhichao Wang, Xin Zhou. 2023-05-15. Existence of four minimal spheres in $S^3$ with a bumpy metric. https://arxiv.org/abs/2305.08755

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