39 citations · 205 across the 34 of their papers we have counts for
32 papers · 1 filter
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 classical minimal surfaces in and -manifolds
Da Rong Cheng, Xin Zhou
We prove that every closed Riemannian or -manifold contains a branched immersed closed minimal surface. That is, there exists a non-constant weakly conformal harmonic ma…
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…
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…
The Half-Volume Spectrum of a Manifold
Liam Mazurowski, Xin Zhou
We define the half-volume spectrum of a closed manifold . This is analogous to the usual volume spectrum of , except that we restr…
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…