Results 21 to 30 of about 358,289 (300)
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, D, Dominic Joyce, Joyce, Dominic
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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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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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Non-linear isocurvature perturbations and non-Gaussianities [PDF]
, 2008 24 pagesWe study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended $\delta N$ formalism, we analyse in detail two illustrative examples. The first is
Vernizzi, F. +4 more
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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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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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LARGE SOLUTIONS FOR YAMABE AND SIMILAR PROBLEMS ON DOMAINS IN RIEMANNIAN MANIFOLDS [PDF]
, 2011 We present a unified approach to study large positive solutions (i.e., u(x) -> infinity as x -> partial derivative Omega) of the equation Delta u + hu - k psi(u) = -f in an arbitrary domain Omega.
Martin Dindoš, Dindos, Martin; id_orcid
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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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Erratum to: Total Scalar Curvature and Harmonic Curvature
Taiwanese Journal of Mathematics, 2016 It has been realized that the proof of Theorem 5.1 in Section 5 is imcomplete. It was pointed out by Professor Jongsu Kim and Israel Evangelista.
Yun, Gabjin +2 more
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