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math.DG2026
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…
math.DG2026
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…
math.DG2026
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…