4 citations · 7 across the 6 of their papers we have counts for
7 papers
Quantitative Volume Estimate on Singular Sets of One-phase Free Boundary Problems in Ricci Limit Spaces
Alejandro Bellati, Kai-Hsiang Wang
We study limit solutions of the one-phase free boundary problem on noncollapsed Ricci limit spaces. We introduce a quantitative stratification of th…
Lower Bound for Weighted Intermediate Ricci Curvature and Tensorial Entropy Convexity
Chao-Ming Lin, Kai-Hsiang Wang
We introduce a weighted version of intermediate Ricci curvature and establish several equivalent characterizations of its lower bound. As an application, we generalize the results…
Dimension Bound of Singular Set of One-Phase Free Boundary Problems in Spaces with Two-Sided Ricci Bound
Kai-Hsiang Wang
In this article, we show that for one-phase free boundary problems in noncollapsed limits of -dimensional manifolds with two-sided Ricci curvature bounds, the Hausdorff dimensio…
On the Probabilistic Approximation in Reproducing Kernel Hilbert Spaces
Dongwei Chen, Kai-Hsiang Wang
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumpt…
Lower Ricci Curvature and Nonexistence of Manifold Structure
Erik Hupp, Aaron Naber, Kai-Hsiang Wang
It is known that a limit of manifolds with uniform lower bounds on Ricci curvature must be -rectifiable for some unique $\dim X:= k\leq n = \dim M…
Optimal Transport Approach to Michael-Simon-Sobolev Inequalities in Manifolds with Intermediate Ricci Curvature Lower Bounds
Kai-Hsiang Wang
We generalize McCann's theorem of optimal transport to a submanifold setting and prove Michael-Simon-Sobolev inequalities for submanifolds in manifolds with lower bounds on interme…
An Isoperimetric-Type Inequality for Spacelike Submanifold in the Minkowski Space
Chung-Jun Tsai, Kai-Hsiang Wang
We prove an isoperimetric-type inequality for maximal, spacelike submanifold in the Minkowski space. The argument is based on the recent work of Brendle.