Results 1 to 10 of about 693,970 (340)
On scalar curvature lower bounds and scalar curvature measure [PDF]
Advances in Mathematics, 2021 We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a Ricci flow solution.
John Lott
semanticscholar +5 more sources
Constraints on primordial curvature spectrum from primordial black holes and scalar-induced gravitational waves [PDF]
European Physical Journal C: Particles and Fields, 2023 The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it
Zhu Yi, Qin Fei
doaj +2 more sources
Mean Curvature in the Light of Scalar Curvature [PDF]
Annales de l'Institut Fourier, 2018 We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
M. Gromov
semanticscholar +5 more sources
Scalar curvature in discrete gravity
European Physical Journal C: Particles and Fields, 2022 We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings.
Ali H. Chamseddine +2 more
doaj +3 more sources
Boundary Conditions for Scalar Curvature [PDF]
, 2020 Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation
Christian Baer, B. Hanke
semanticscholar +3 more sources
On Scalar and Ricci Curvatures [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2020 The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds carry a complete Riemannian metric of positive or non negative scalar curvature?
Gérard Besson, Sylvestre Gallot
openalex +5 more sources
Scalar curvature and $Q$-curvature of random metrics [PDF]
The Journal of Geometric Analysis, 2010 We study Gauss curvature for random Riemannian metrics on a compact surface, lying in a fixed conformal class; our questions are motivated by comparison geometry. Next, analogous questions are considered for the scalar curvature in dimension $n>2$, and for the $Q$-curvature of random Riemannian metrics.
Yaiza Canzani +2 more
openalex +6 more sources
Metric Inequalities with Scalar Curvature [PDF]
Geometric and Functional Analysis, 2017 We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is concerned these inequalities appear as generalisations of the classical bounds on ...
M. Gromov
semanticscholar +4 more sources
A Splitting Theorem for Scalar Curvature [PDF]
Communications on Pure and Applied Mathematics, 2018 We show that a Riemannian 3‐manifold with nonnegative scalar curvature is flat if it contains an area‐minimizing cylinder. This scalar‐curvature analogue of the classical splitting theorem of J. Cheeger and D. Gromoll (1971) was conjectured by D. Fischer‐
Otis Chodosh, M. Eichmair, Vlad Moraru
semanticscholar +5 more sources
Scalar curvature of Lie groups [PDF]
Proceedings of the American Mathematical Society, 1981 In this paper, we prove the following theorem: If G G is a connected Lie group, then G G admits left invariant metric of positive scalar curvature if and only if the universal covering space G ~ \tilde G of G G is not homeomorphic to the ...
Hêng Lung Lai, Huei Shyong Lue
openalex +2 more sources