Related papers: A positive mass theorem in three dimensional Cauch…
We consider three dimensional gravity with a positive cosmological constant and non- zero gravitational Chern-Simons term. This theory has inflating de Sitter solutions and local metric degrees of freedom. The Euclidean signature partition…
We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang; and the Jang equation in Schoen-Yau, Eichmair and Jang. Then, we proved a…
We derive the Riemannian Positive Mass theorem in arbitrary dimensions, without any topological constraints. The main new tools are skin structures and surgeries on minimal hypersurfaces.
The CR Paneitz operator is closely related to some important problems in CR geometry. In this paper, we consider this operator on a non-embeddable CR manifold. This operator is essentially self-adjoint and its spectrum is discrete except…
We consider the porous medium equation (PME) on complete noncompact manifolds $M$ of nonnegative Ricci curvature. We require nonparabolicity of the manifold and construct a natural space $X$ of functions, strictly larger than $L^1$, in…
We study the space of smooth Riemannian structures on compact three-manifolds with boundary that satisfies a critical point equation associated with a boundary value problem, for simplicity, Miao-Tam critical metrics. We provide an estimate…
We solve $\square_b$ on a class of non-compact 3-dimensional strongly pseudoconvex CR manifolds via a certain conformal equivalence. The idea is to make use of a related $\square_b$ operator on a compact 3-dimensional strongly pseudoconvex…
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 corresponding stability theorem for spaces that can be…
In this paper we take an approach similar to that in [M] to establish a positive mass theorem for asymptotically hyperbolic spin manifolds admitting corners along a hypersurface. The main analysis uses an integral representation of a…
We give an integral formula for the total $Q^\prime$-curvature of a three-dimensional CR manifold with positive CR Yamabe constant and nonnegative Paneitz operator. Our derivation includes a relationship between the Green's functions of the…
In this work, we readdress the Dirac equation in the position-dependent mass (PDM) scenario. Here, one investigates the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming a $(1+1)$-dimension flat spacetime.…
We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive…
Let $(M, g)$ be an asymptotically flat Riemannian $3$-manifold with non-negative scalar curvature and positive mass. We show that each leaf of the canonical foliation through stable constant mean curvature surfaces of the end of $(M, g)$ is…
In this paper, we revisit the no black hole theorem in three dimensional (3D) gravity in the Newman-Penrose formalism in a generalized Newman-Unti gauge. After adapting the well established 4D NP formalism and its gauge and coordinates…
We formulate noncommutative three-dimensional (3d) gravity by making use of its connection with 3d Chern-Simons theory. In the Euclidean sector, we consider the particular example of topology $T^2 \times R$ and show that the 3d black hole…
We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein)…
For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to…
For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end, while allowing for points of incompleteness (or negative scalar curvature) away from this…
We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still…
In this article we extend several foundational results of the theory of complete minimal surfaces of finite index in the Euclidean space to minimal surfaces in asymptotically flat manifolds and, more generally, to marginally outer-trapped…