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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
Minimal surfaces with low genus in lens spaces
Xingzhe Li, Tongrui Wang, Xuan Yao
Given a Riemannian with a bumpy metric or a metric of positive Ricci curvature, we show that there either exist four distinct minimal real projective planes, or exi…
math.DG2024
Generic Scarring for Minimal Hypersurfaces in Manifolds Thick at Infinity with a Thin Foliation at Infinity
Xingzhe Li
We show generic scarring phenomenon for minimal hypersurfaces in a class of complete non-compact manifolds. In particular, we prove that for any metric in a -generi…