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math.DG2024
Existence of embedded minimal tori in three-spheres with positive Ricci curvature
Xingzhe Li, Zhichao Wang
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…
math.DG2024
Scalar-mean rigidity theorem for compact manifolds with boundary
Jinmin Wang, Zhichao Wang, Bo Zhu
We prove a scalar-mean rigidity theorem for compact Riemannian manifolds with boundary in dimension less than five by developing a dimension reduction argument for mean curvature,…