45 citations · 222 across the 25 of their papers we have counts for
26 papers
Equality in the spacetime positive mass theorem II
Lan-Hsuan Huang, Dan A. Lee
We provide a new proof of the equality case of the spacetime positive mass theorem, which states that if a complete asymptotically flat initial data set satisfying the…
Static vacuum extensions with prescribed Bartnik boundary data near a general static vacuum metric
Zhongshan An, Lan-Hsuan Huang
We introduce the notions of static regular of type (I) and type (II) and show that they are sufficient conditions for local well-posedness of solving asymptotically flat, static va…
New asymptotically flat static vacuum metrics with near Euclidean boundary data
Zhongshan An, Lan-Hsuan Huang
In our prior work toward Bartnik's static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm larg…
Scalar curvature deformation and mass rigidity for ALH manifolds with boundary
Lan-Hsuan Huang, Hyun Chul Jang
We study scalar curvature deformation for asymptotically locally hyperbolic (ALH) manifolds with nonempty compact boundary. We show that the scalar curvature map is locally surject…
Existence of static vacuum extensions with prescribed Bartnik boundary data
Zhongshan An, Lan-Hsuan Huang
We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to the induced boundary d…
Intrinsic flat convergence of points and applications to stability of the positive mass theorem
Lan-Hsuan Huang, Dan A. Lee, Raquel Perales
We prove results on intrinsic flat convergence of points---a concept first explored by Sormani in \cite{Sormani-AA}. In particular, we discuss compatibility with Gromov-Hausdorff c…
Bartnik mass minimizing initial data sets and improvability of the dominant energy scalar
Lan-Hsuan Huang, Dan A. Lee
We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initi…
Mass rigidity for hyperbolic manifolds
Lan-Hsuan Huang, Hyun Chul Jang, Daniel Martin
We prove the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality holds, then the manifold is isometric to hyperbolic space. The…
Static potentials and area minimizing hypersurfaces
Lan-Hsuan Huang, Daniel Martin, Pengzi Miao
We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if…
Equality in the Spacetime Positive Mass Theorem
Lan-Hsuan Huang, Dan A. Lee
We affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight. Namely, if an asymptotically flat initial data set satisfies the dominant en…
Existence of harmonic maps into CAT(1) spaces
Christine Breiner, Ailana Fraser, Lan-Hsuan Huang +3
Let where is a compact Riemann surface, is a compact locally CAT(1) space, and is defined as in Korevaar-Schoen. We use the tec…
Regularity of Harmonic Maps from Polyhedra to CAT(1) Spaces
Christine Breiner, Ailana Fraser, Lan-Hsuan Huang +3
We determine regularity results for energy minimizing maps from an -dimensional Riemannian polyhedral complex into a CAT(1) space. Provided that the metric on is Lipschi…
Localized deformation for initial data sets with the dominant energy condition
Justin Corvino, Lan-Hsuan Huang
We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be…
Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
Lan-Hsuan Huang, Dan A. Lee, Christina Sormani
The rigidity of the Positive Mass Theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We study the…
Stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
Lan-Hsuan Huang, Dan A. Lee
The rigidity of the positive mass theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We prove a co…
On the validity of the definition of angular momentum in general relativity
Po-Ning Chen, Lan-Hsuan Huang, Mu-Tao Wang +1
We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime…
The equality case of the Penrose inequality for asymptotically flat graphs
Lan-Hsuan Huang, Damin Wu
We prove the equality case of the Penrose inequality in all dimensions for asymptotically flat hypersurfaces. It was recently proven by G. Lam that the Penrose inequality holds for…
The spacetime positive mass theorem in dimensions less than eight
Michael Eichmair, Lan-Hsuan Huang, Dan A. Lee +1
We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy con…
Geometric inequalities and rigidity theorems on equatorial spheres
Lan-Hsuan Huang, Damin Wu
We prove rigidity for hypersurfaces with boundary in the unit -sphere with scalar curvature bounded below by . Under appropriate boundary conditions, the hypersurfac…
Hypersurfaces with nonnegative scalar curvature
Lan-Hsuan Huang, Damin Wu
We show that closed hypersurfaces in Euclidean space with nonnegative scalar curvature are weakly mean convex. In contrast, the statement is no longer true if the scalar curvature…
On the center of mass in general relativity
Lan-Hsuan Huang
The classical notion of center of mass for an isolated system in general relativity is derived from the Hamiltonian formulation and represented by a flux integral at infinity. In c…
Specifying angular momentum and center of mass for vacuum initial data sets
Lan-Hsuan Huang, Richard Schoen, Mu-Tao Wang
We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and a…
Solutions of special asymptotics to the Einstein constraint equations
Lan-Hsuan Huang
We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat…
Rigidity theorems on hemispheres in non-positive space forms
Lan-Hsuan Huang, Damin Wu
We study the curvature condition which uniquely characterizes the hemisphere. In particular, we prove the Min-Oo conjecture for hypersurfaces in Euclidean space and hyperbolic spac…