Home » Lan-Hsuan Huang

Personal Profile of Lan-Hsuan Huang

Lan-Hsuan Huang

University of Connecticut

Department of Mathematics

University of Connecticut

Department of Mathematics

Home Page: https://lhhuang.math.uconn.edu

ORCID: https://orcid.org/0000-0002-8918-3071

• Talks

1. November 18, 2013 - November 22, 2013

   Workshop Initial Data and Evolution Problems in General Relativity

   Show All Collapse

   Nov 18, 2013 Monday

   02:20 PM - 03:15 PM   Asymptotically Flat Graphs with Small Mass Lan-Hsuan Huang (University of Connecticut) Location MSRI: Simons Auditorium Video -- Abstract The Riemannian positive mass theorem and its rigidity is recently proven for asymptotically flat hypersurfaces in Euclidean space in all dimensions. The rigidity says that the hyperplane is the only asymptotically flat hypersurface with nonnegative scalar curvature whose ADM mass is zero. In this talk, we consider a class of asymptotically flat graphs with small positive mass and show that the graph is effectively close to a hyperplane if the mass is small. This is a joint work with Dan Lee Supplements Huang 178 KB application/pdf Show Detail

2. September 09, 2013 - September 13, 2013

   Workshop Introductory Workshop: Mathematical Relativity

   Show All Collapse

   Sep 12, 2013 Thursday

   02:00 PM - 03:00 PM   Density Theorems for the Einstein Constraint Equations Lan-Hsuan Huang (University of Connecticut) Location MSRI: Simons Auditorium Video Abstract We will start with a beautiful theorem of Corvino and Schoen which says that the asymptotically flat initial data sets with harmonic asymptotics are dense among general initial data sets. Then we will discuss several generalizations of the density theorem and their applications in the positive mass theorem and the constructions relating to the center of mass and angular momentum. Supplements Notes 155 KB application/pdf Show Detail

3. September 03, 2013 - September 04, 2013

   Workshop Connections for Women: Mathematical General Relativity

   Show All Collapse

   Sep 03, 2013 Tuesday

   09:00 AM - 10:00 AM   Hypersurfaces with non-negative scalar curvature Lan-Hsuan Huang (University of Connecticut) Location MSRI: Simons Auditorium Video Abstract Since the time of Gauss, geometers have been interested in the interplay between the intrinsic structure of hypersurfaces and their extrinsic geometry from the ambient space. Many classical results discuss the sectional curvature. For example, it is known that a complete hypersurface in Euclidean space with non-negative sectional curvature is either convex or a generalized hypercylinder. In a series of joint work with Damin Wu, we study hypersurfaces with non-negative scalar curvature. We prove that a closed hypersurface with nonnegative scalar curvature must be weakly mean convex. In general, vanishing scalar curvature causes analytical difficulties because the scalar curvature operator may not be elliptic. We tackle the problem by studying the level sets of a height function, which is motivated by general relativity. We further extend our proof to unbounded hypersurfaces which are asymptotically flat at infinity and obtain applications in the positive mass theorem and the Penrose inequality. Supplements Huang 215 KB application/pdf Show Detail