7 papers
Existence of two embedded minimal spheres in with an arbitrary metric
Zhichao Wang, Xin Zhou
We prove that endowed with an arbitrary Riemannian metric admits at least two embedded minimal spheres. The proof is based on an iterative scheme of relative min-max cons…
Existence of free boundary minimal disks in convex regions
Lorenzo Sarnataro, Douglas Stryker, Zhichao Wang +1
We show that any three-ball with mean convex boundary contains an embedded free boundary minimal disk. Moreover, when the three-ball is a strictly convex domain with nonnegative Ri…
Equivariant min-max theory and the spherical Bernstein problem in
Tongrui Wang, Zhichao Wang, Xin Zhou
We construct an embedded non-equatorial minimal hypersphere in the unit -sphere , which provides a new resolution of Chern's spherical Bernstein problem in $\mathb…
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,…
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…
Improved regularity for multiple membranes problem
Zhichao Wang, Xin Zhou
We prove the -regularity for stationary () solutions to the multiple membrane problem. This regularity estimate was essentially used in our recent w…