33 citations · 94 across the 12 of their papers we have counts for
12 papers
Decomposing 4-manifolds with positive scalar curvature
Richard H. Bamler, Chao Li, Christos Mantoulidis
We show that every closed, oriented, topologically PSC 4-manifold can be obtained via 0 and 1-surgeries from a topologically PSC 4-orbifold with vanishing first Betti number and se…
Min-max theory for capillary surfaces
Chao Li, Xin Zhou, Jonathan J. Zhu
We develop a min-max theory for the construction of capillary surfaces in 3-manifolds with smooth boundary. In particular, for a generic set of ambient metrics, we prove the existe…
Metrics with and flexibility in the Riemannian Penrose Inequality
Chao Li, Christos Mantoulidis
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectra…
Generalized soap bubbles and the topology of manifolds with positive scalar curvature
Otis Chodosh, Chao Li
We prove that for , a closed aspherical -manifold does not admit a Riemannian metric with positive scalar curvature. Additionally, we show that for , the…
Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces
Chao Li
In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedrons enclosed by horospheres in hyperbolic manifolds, extending Gromov's comparison…
Regularity of free boundary minimal surfaces in locally polyhedral domains
Nicholas Edelen, Chao Li
We prove an Allard-type regularity theorem for free-boundary minimal surfaces in Lipschitz domains locally modelled on convex polyhedra. We show that if such a minimal surface is s…
The dihedral rigidity conjecture for n-prisms
Chao Li
We prove the following comparison theorem for metrics with nonnegative scalar curvature, also known as the dihedral rigidity conjecture by Gromov: for , if an -dimension…
Constrained deformations of positive scalar curvature metrics
Alessandro Carlotto, Chao Li
We present a series of results concerning the interplay between the scalar curvature of a manifold and the mean curvature of its boundary. In particular, we give a complete topolog…
A polyhedron comparison theorem for 3-manifolds with positive scalar curvature
Chao Li
The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, an…
Positive scalar curvature with skeleton singularities
Chao Li, Christos Mantoulidis
We study positive scalar curvature on the regular part of Riemannian manifolds with singular, uniformly Euclidean () metrics that consolidate Gromov's scalar curvature po…
Global regularity and fast small scale formation for Euler patch equation in a disk
Chao Li
It is well known that the Euler vortex patch in will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solution…
Index and topology of minimal hypersurfaces in R^n
Chao Li
In this paper, we consider immersed two-sided minimal hypersurfaces in with finite total curvature. We prove that the sum of the Morse index and the nullity of the J…