Results 11 to 20 of about 298,518 (247)
Localized gluing of Riemannian metrics in interpolating their scalar curvature [PDF]
arXiv, 2010 We show that two smooth nearby Riemannian metrics can be glued interpolating their scalar curvature. The resulting smooth metric is the same as the starting ones outside the gluing region and has scalar curvature interpolating between the original ones. One can then glue metrics while maintaining inequalities satisfied by the scalar curvature.
Delay, Erwann
arxiv +4 more sources
On positive scalar curvature bordism
Communications in Analysis and Geometry, 2022 Using standard results from higher (secondary) index theory, we prove that the positive scalar curvature bordism groups of a cartesian product GxZ are infinite in dimension 4n if n>0 G a group with non-trivial torsion. We construct representatives of each of these classes which are connected and with fundamental group GxZ.
Piazza, Paolo +2 more
openaire +3 more sources
On the scalar curvature of Einstein manifolds [PDF]
Mathematical Research Letters, 1997 LaTeX.
Catanese, Fabrizio, LeBrun, Claude
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On scalar curvature lower bounds and scalar curvature measure
Advances in Mathematics, 2022 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.
openaire +2 more sources
Mean Curvature in the Light of Scalar Curvature [PDF]
Annales de l'Institut Fourier, 2020 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.
openaire +3 more sources
A Splitting Theorem for Scalar Curvature [PDF]
Communications on Pure and Applied Mathematics, 2018 AbstractWe 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‐Colbrie and R. Schoen (1980) and by M. Cai and G. Galloway (2000).
Otis Chodosh +2 more
openaire +4 more sources
Volume and macroscopic scalar curvature [PDF]
Geometric and Functional Analysis, 2021 AbstractWe prove the macroscopic cousins of three conjectures: (1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, (2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, (3) a conjectural bound of$$\ell ^2$$ℓ2-Betti numbers of ...
Braun, Sabine, Sauer, Roman
openaire +3 more sources
Electronic Research Archive, 2022 We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean ...
Marco G. Ghimenti +1 more
doaj +1 more source
Boundary Conditions for Scalar Curvature
, 2023 Minor typos fixed.
Bernhard Hanke, Christian Bär
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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.
Igor Wigman +3 more
openaire +5 more sources