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Bibliographische Detailangaben
Hauptverfasser: Li, Xingzhe, Wang, Zhichao
Format: Preprint
Veröffentlicht: 2024
Schlagworte:
Online-Zugang:https://arxiv.org/abs/2409.10391
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  • In this paper, we prove the strong Morse inequalities for the area functional in the space of embedded tori and spheres in the three sphere. As a consequence, we prove that in the three dimensional sphere with positive Ricci curvature, there exist at least 4 distinct embedded minimal tori. Suppose in addition that the metric is bumpy, then the three-sphere contains at least 9 distinct embedded minimal tori. The proof relies on a multiplicity one theorem for the Simon-Smith min-max theory proved by the second author and X. Zhou.