Xin Zhou

collaborators

4 papers

math.DG2026

Existence of two embedded minimal spheres in $S^{3}$ with an arbitrary metric

Zhichao Wang, Xin Zhou

We prove that $S^{3}$ endowed with an arbitrary Riemannian metric $g$ admits at least two embedded minimal spheres. The proof is based on an iterative scheme of relative min-max cons…

math.DG2026

Existence of classical minimal surfaces in $4$ and $5$ -manifolds

Da Rong Cheng, Xin Zhou

We prove that every closed Riemannian $4$ or $5$ -manifold $M$ contains a branched immersed closed minimal surface. That is, there exists a non-constant weakly conformal harmonic ma…

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

Mass- $p$ -Capacity Inequalities in Asymptotically Flat Half-Spaces

Chao Xia, Jiabin Yin, Xingjian Zhou

In this paper, we establish general monotone quantities and sharp mass-capacity inequalities related to $p$ -capacitary functions in $3$ -dimensional asymptotically flat half-spaces…

Existence of two embedded minimal spheres in S3 with an arbitrary metric

Existence of classical minimal surfaces in 4 and 5-manifolds

Existence of free boundary minimal disks in convex regions

Mass-p-Capacity Inequalities in Asymptotically Flat Half-Spaces

Existence of two embedded minimal spheres in $S^{3}$ with an arbitrary metric

Existence of classical minimal surfaces in $4$ and $5$ -manifolds

Mass- $p$ -Capacity Inequalities in Asymptotically Flat Half-Spaces