Topic
Scalar curvature
About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.
Papers published on a yearly basis
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TL;DR: In this article, it was shown that (M, g) is ℂℙ2 with its standard Fubini-Study metric, up to rescaling and isometry.
Abstract: Let (M, g) be a compact oriented four-dimensional Einstein manifold. If M has positive intersection form and g has non-negative sectional curvature, we show that, up to rescaling and isometry, (M, g) is ℂℙ2, with its standard Fubini–Study metric.
91 citations
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TL;DR: In this paper, a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem are studied. But their focus is mainly on a conformal metric on a given Riemannian manifold.
Abstract: The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the Yamabe problem and the corresponding Liouville type problem.
91 citations
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TL;DR: In this article, the existence of Euclidean tangent cones on Wasserstein spaces over compact Alexandrov spaces of curvature bounded below was established by using Riemannian structure.
Abstract: We establish the existence of Euclidean tangent cones on Wasserstein
spaces over compact Alexandrov spaces of curvature bounded below. By
using this Riemannian structure, we formulate and construct gradient
flows of functions on such spaces. If the underlying space is a
Riemannian manifold of nonnegative sectional curvature, then our
gradient flow of the free energy produces a solution of the linear
Fokker-Planck equation.
91 citations
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91 citations
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TL;DR: In this paper, the authors characterize the topology of 3D Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension.
Abstract: The purpose of this paper is to completely characterize the topology of three-dimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension.
91 citations