Xingzhe Li

activity

20242026

collaborators

4 papers

math.DG2026

Infinite existence of equivariant minimal hypersurfaces

Xingzhe Li, Tongrui Wang

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show that there are infinitely many $G$ -invariant minimal hypersurfaces. Under the assump…

math.DG2025

Area Rigidity for the Regular Representation of Surface Groups

Riccardo Caniato, Xingzhe Li, Antoine Song

Let $I^~ £$ be the universal cover of a closed surface $I^£$ of genus at least $2$ . We characterize all equivariantly area-minimizing maps from $I^~ £$ to a Hilbert sphere, wh…

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 $RP^{3}$ 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…