Related papers: Positive mass theorem for the Paneitz-Branson oper…

We present a streamlined, complete proof, valid in arbitrary space dimension $n$, and using only spinors on the oriented Riemannian space $(M^{n};g),$ of the positive energy theorem in General Relativity.

In this paper, we consider compact graphical manifolds with boundary over (locally) hyperbolic static space. We prove the stability of the positive mass theorem with respect to the Federer--Fleming flat distance for the static quasi-local…

We investigate the curvature operator of the second kind on Riemannian manifolds and prove several classification results. The first one asserts that a closed Riemannian manifold with three-positive curvature operator of the second kind is…

We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space $W^{2, n/2}_{loc}$ for manifolds of dimension less than or equal to $7$ or spin-manifolds of any dimension. More generally, we give…

In this paper, we prove a positive mass theorem and Penrose-type inequality of the Gauss-Bonnet-Chern mass $m_2$ for the graphic manifold with flat normal bundle.

The Dirac-Dolbeault operator for a compact K\"ahler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows to express the values of the sections of the…

Let $(M^4,\bar{g})$ be an Einstein manifold, where $M^4$ is a smooth, closed, oriented four-manifold $M^4$ and $\bar{g}$ has positive Einstein constant. Given a point $0 \in M^4$, let $G$ denote the (positive) Green's function $G$ of the…

Work of D. Stern and Bray-Kazaras-Khuri-Stern provide differential-geometric identities which relate the scalar curvature of Riemannian 3-manifolds to global invariants in terms of harmonic functions. These quantitative formulas are useful…

Let $(M,g)$ be a compact Riemannian manifold with non-empty boundary. Provided $f$ an isoparametric function of $(M,g)$ we prove existence results for positive solutions of the Yamabe equation that are constant along the level sets of $f$.…

The rigidity of the Riemannian positive mass theorem for asymptotically hyperbolic manifolds states that the total mass of such a manifold is zero if and only if the manifold is isometric to the hyperbolic space. This leads to study the…

We show a spacetime positive mass theorem for asymptotically flat initial data sets with a noncompact boundary. We develop a mass type invariant and a boundary dominant energy condition. Our proof is based on spinors.

This paper proves a positive energy-momentum theorem for oriented Riemannian 3-manifolds that are asymptotic to a standard hyperbolic slice in anti de Sitter space-time. Analogously to the original Witten's proof in the asymptotically flat…

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…

For a compact subgroup $G$ of the group of isometries acting on a Riemannian manifold $M$ we investigate subspaces of Besov and Triebel-Lizorkin type which are invariant with respect to the group action. Our main aim is to extend the…

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or the total space of an orbifiber bundle over $\mathbb{S}^1$…

We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in…

In this paper, we prove a gap result for a locally conformally flat complete non-compact Riemannian manifold with bounded non-negative Ricci curvature and a scalar curvature average condition. We show that if it has positive Green function,…

In this paper we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same…

Let $M$ be a compact, pseudoconvex-oriented, $(2n+1)$-dimensional, abstract CR manifold of hypersurface type, $n\geq 2$. We prove the following: (i) If $M$ admits a strictly CR-plurisubharmonic function on $(0,q_0)$-forms, then the complex…

We characterize the positive Schur property in the positive projective tensor products of Banach lattices, we establish the connection with the weak operator topology and we give necessary and sufficient conditions for the space of regular…