Results 21 to 30 of about 13,851 (306)
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.
Canzani, Yaiza +2 more
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Horizon curvature and spacetime structure influences on black hole scalarization
European Physical Journal C: Particles and Fields, 2021 Black hole spontaneous scalarization has been attracting more and more attention as it circumvents the well-known no-hair theorems. In this work, we study the scalarization in Einstein–scalar-Gauss–Bonnet theory with a probe scalar field in a black hole ...
Hong Guo +3 more
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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 bounds on their scalar curvatures, and prove a few theorems motivating these ...
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ON THE FLAG CURVATURE OF FINSLER METRICS OF SCALAR CURVATURE [PDF]
Journal of the London Mathematical Society, 2003 23 ...
Chen, Xinyue +2 more
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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. 0.1 0.1
Bolotov, Dmitry, Dranishnikov, Alexander
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A Splitting Theorem for Scalar Curvature [PDF]
Communications on Pure and Applied Mathematics, 2018 Abstract 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‐Colbrie and R. Schoen (1980) and by M.
Chodosh, Otis +2 more
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Metrics of constant negative scalar-Weyl curvature [PDF]
, 2023 Extending Aubin's construction of metrics with constant negative scalar curvature, we prove that every n-dimensional closed manifold admits a Riemannian metric with constant negative scalarWeyl curvature, that is R + t|W|, t is an element of R.
Catino, Giovanni
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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.
Corvino, Justin +2 more
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On the singular prescribed scalar curvature problem [PDF]
, 2023 Let (M, g) be a compact Riemannian manifold of dimension \(n \geq3\). In this paper, we define and introduce the prescribed scalar curvature problem with singularities. Under some assumptions, we show that there exists a conformal metric \(\overline{g}\)
Hichem Boughazi
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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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