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Infinite existence of equivariant minimal hypersurfaces
Xingzhe Li, Tongrui Wang
For a closed Riemannian manifold with a compact Lie group acting by isometries, we show that there are infinitely many -invariant minimal hypersurfaces. Under the assump…
Area Rigidity for the Regular Representation of Surface Groups
Riccardo Caniato, Xingzhe Li, Antoine Song
Let be the universal cover of a closed surface of genus at least . We characterize all equivariantly area-minimizing maps from to a Hilbert sphere, which…
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…
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…
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…