Results 21 to 30 of about 292,024 (345)
On Gromov’s scalar curvature conjecture [PDF]
Proceedings of the American Mathematical Society, 2009 We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on the fundamental group.0.10.1.Theorem.Suppose that a discrete groupπ\pihas the following properties:11. The Strong Novikov Conjecture holds forπ\pi.22.
Alexander Dranishnikov, Dmitry Bolotov
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Geometric Inequalities for a Submanifold Equipped with Distributions
Mathematics, 2022 The article introduces invariants of a Riemannian manifold related to the mutual curvature of several pairwise orthogonal subspaces of a tangent bundle. In the case of one-dimensional subspaces, this curvature is equal to half the scalar curvature of the
Vladimir Rovenski
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Constant Scalar Curvature Metrics on Connected Sums [PDF]
, 2001 The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension $n \geq 3$, which minimizes the total scalar curvature of this ...
Joyce, Dominic
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Deformations of the scalar curvature
Duke Mathematical Journal, 1975 N ...
Fischer, Arthur E., Marsden, Jerrold E.
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Hypersurfaces with nonnegative scalar curvature [PDF]
Journal of Differential Geometry, 2013 A point in the proof of Theorem 2 that was overlooked in the previous versions is fixed. The appendix of some topological results is added. To appear in J.
Huang, Lan-Hsuan, Wu, Damin
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TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE
Taiwanese Journal of Mathematics, 2014 On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved.
Yun, Gabjin +2 more
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Renormalizable Gravitational Action That Reduces to General Relativity on the Mass-Shell
Galaxies, 2018 We derive the equation that relates gravity to quantum mechanics: R|mass-shell=8πGc4LSM, where R is the scalar curvature, G is the gravitational constant, c is the speed of light and LSM is the Standard Model Lagrangian, or its future replacement ...
Peter D. Morley
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Deformation of scalar curvature and volume [PDF]
Mathematische Annalen, 2013 The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equal to a given constant.
Justin Corvino +3 more
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ON THE FLAG CURVATURE OF FINSLER METRICS OF SCALAR CURVATURE [PDF]
Journal of the London Mathematical Society, 2003 23 ...
Xiaohuan Mo, Xinyue Chen, Zhongmin Shen
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Enlargeable length-structure and scalar curvatures [PDF]
Annals of Global Analysis and Geometry, 2021 AbstractWe define enlargeable length-structures on closed topological manifolds and then show that the connected sum of a closed n-manifold with an enlargeable Riemannian length-structure with an arbitrary closed smooth manifold carries no Riemannian metrics with positive scalar curvature.
Deng, Jialong +1 more
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