39 citations · 205 across the 34 of their papers we have counts for
5 papers · 1 filter
Min-max theory for networks of constant geodesic curvature
Xin Zhou, Jonathan J. Zhu
We prove that on a closed surface, for any , our min-max theory for prescribing mean curvature produces a solution given by a curve of constant geodesic curvature which is…
Existence of hypersurfaces with prescribed mean curvature I - Generic min-max
Xin Zhou, Jonathan J. Zhu
We prove that, for a generic set of smooth prescription functions on a closed ambient manifold, there always exists a nontrivial, smooth, closed hypersurface of prescribed mean…
Min-max minimal disks with free boundary in Riemannian manifolds
Longzhi Lin, Ao Sun, Xin Zhou
In this paper, we establish a min-max theory for constructing minimal disks with free boundary in any closed Riemannian manifold. The main result is an effective version of the par…
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…