arXiv:1908.10612v6 [math.DG] 8 Jul 2021 Page 1 arXiv:1908.10612v6 [math.DG] 8 Jul 2021
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …

The aim of this paper is to discuss convergence of pointed metric measure spaces in the
absence of any compactness condition. We propose various definitions, and show that all of …

We show that the Euclidean 3-space\(\mathbb {R}^{3}\) is stable for the Positive Mass
Theorem in the following sense. Let\((M_ {i}, g_ {i})\) be a sequence of complete …

Groping our way toward a theory of singular spaces with positive scalar curvatures we look
at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with …

Here we survey the compactness and geometric stability conjectures formulated by the
participants at the 2018 IAS Emerging Topics Workshop on Scalar Curvature and …

The null distance of Sormani and Vega encodes the manifold topology as well as the
causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length …

Llarull's theorem characterizes the round sphere S n among all spin manifolds whose scalar
curvature is bounded from below by n (n− 1). In this paper we show that if the scalar …

Consider a sequence of Riemannian manifolds (M in, gi) whose scalar curvatures and
entropies are bounded from below by small constants R i, μ i≥− 𝜖 i. The goal of this paper is …

We present an abstract approach to Lorentzian Gromov–Hausdorff distance and
convergence, and an alternative approach to Lorentzian length spaces that does not use …

We study the stability of the positive mass theorem using the intrinsic flat distance. In
particular we consider the class of complete asymptotically flat rotationally symmetric …