18 citations · 47 across the 19 of their papers we have counts for
20 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…
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…
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,…
On the waist and width inequality in complete 3-manifolds with positive scalar curvature
Yevgeny Liokumovich, Zhichao Wang
We show that a complete non-compact 3-manifold with scalar curvature bounded below by a positive constant admits a singular foliation by surfaces of controlled area and diameter.
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 wor…
Existence of four minimal spheres in with a bumpy metric
Zhichao Wang, Xin Zhou
We prove that in the three dimensional sphere with a bumpy metric or a metric with positive Ricci curvature, there exist at least four distinct embedded minimal two-spheres. This c…
Min-max minimal hypersurfaces with higher multiplicity
Zhichao Wang, Xin Zhou
We exhibit the first set of examples of non-bumpy metrics on the -sphere () in which the varifold associated with the two-parameter min-max construction must…
Uryson width of three dimensional mean convex domain with non-negative Ricci curvature
Zhichao Wang, Bo Zhu
We prove that for every three dimensional manifold with nonnegative Ricci curvature and strictly mean convex boundary, there exists a Morse function so that each connected componen…
Conformal upper bounds for the volume spectrum
Zhichao Wang
In this paper, we prove upper bounds for the volume spectrum of a Riemannian manifold that depend only on the volume, dimension and a conformal invariant.
Multiplicity one for min-max theory in compact manifolds with boundary and its applications
Ao Sun, Zhichao Wang, Xin Zhou
We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approa…
Existence of infinitely many free boundary minimal hypersurfaces
Zhichao Wang
In this paper, we prove that in any compact Riemannian manifold with smooth boundary, of dimension at least 3 and at most 7, there exist infinitely many almost properly embedded fr…
Existence of minimal hypersurfaces with non-empty free boundary for generic metrics
Zhichao Wang
For almost all Riemannian metrics (in the Baire sense) on a compact manifold with boundary , , we prove that, for any open sub…
Min-max theory for free boundary minimal hypersurfaces II -- General Morse index bounds and applications
Qiang Guang, Martin Man-chun Li, Zhichao Wang +1
For any smooth Riemannian metric on an -dimensional compact manifold with boundary where , we establish general upper bounds for the Mors…
Compactness and generic finiteness for free boundary minimal hypersurfaces (II)
Zhichao Wang
Given a compact Riemannian manifold with boundary, we prove that the limit of a sequence of embedded, almost properly embedded free boundary minimal hypersurfaces, with uniform are…
Compactness of self-shrinkers in with fixed genus
Ao Sun, Zhichao Wang
We prove the compactness of self-shrinkers in with bounded entropy and fixed genus. As a corollary, we show that numbers of ends of such surfaces are uniformly bounde…
Compactness and generic finiteness for free boundary minimal hypersurfaces (I)
Qiang Guang, Zhichao Wang, Xin Zhou
Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index…
Free boundary minimal hypersurfaces with least area
Qiang Guang, Zhichao Wang, Xin Zhou
In this paper, we prove the existence of the free boundary minimal hypersurface of least area in compact manifolds with boundary. Such hypersurface can be viewed as the ground stat…
Min-max minimal hypersurface in manifolds with convex boundary and
Zhichao Wang
Let be a compact manifold with non-negative Ricci curvature, convex boundary and . We show that the min-max minimal hypersurface with respec…