39 citations · 205 across the 34 of their papers we have counts for
5 papers · 1 filter
Sweeping out 3-manifold of positive Ricci curvature by short 1-cycles via estimates of min-max surfaces
Yevgeny Liokumovich, Xin Zhou
We prove that given a three manifold with an arbitrary metric of positive Ricci curvature, there exists a sweepout of by surfaces of genus and areas bounded…
Entropy of closed surfaces and min-max theory
Daniel Ketover, Xin Zhou
Entropy is a natural geometric quantity measuring the complexity of a surface embedded in . For dynamical reasons relating to mean curvature flow, Colding-Ilmanen-Min…
On the free boundary min-max geodesics
Xin Zhou
Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we dev…
Existence of minimal surfaces of arbitrary large Morse index
Haozhao Li, Xin Zhou
We show that in a closed 3-manifold with a generic metric of positive Ricci curvature, there are minimal surfaces of arbitrary large Morse index, which partially confirms a conject…
Min-max hypersurface in manifold of positive Ricci curvature
Xin Zhou
In this paper, we study the shape of the min-max minimal hypersurface produced by Almgren-Pitts-Schoen-Simon \cite{AF62, AF65, P81, SS81} in a Riemannian manifold of…