Displaying similar documents to “On the finiteness of the fundamental group of a compact shrinking Ricci soliton”

De Lellis-Topping type inequalities for f-Laplacians

Guangyue Huang, Fanqi Zeng (2016)

Studia Mathematica

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We establish an integral geometric inequality on a closed Riemannian manifold with ∞-Bakry-Émery Ricci curvature bounded from below. We also obtain similar inequalities for Riemannian manifolds with totally geodesic boundary. In particular, our results generalize those of Wu (2014) for the ∞-Bakry-Émery Ricci curvature.

Characterization of Low Dimensional RCD*(K, N) Spaces

Yu Kitabeppu, Sajjad Lakzian (2016)

Analysis and Geometry in Metric Spaces

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In this paper,we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called RCD*(K, N) spaces) with non-empty one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with Ric ≥ K and Hausdorff dimension N and the class of RCD*(K, N) spaces coincide for N < 2 (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality (that is ,roughly speaking,...

Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix

Yana Alexieva, Stefan Ivanov (1999)

Archivum Mathematicum

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Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures r 1 = r 2 = 0 , r 3 ≠ 0 , which are not locally homogeneous, in general.

Curvature cones and the Ricci flow.

Thomas Richard (2012-2014)

Séminaire de théorie spectrale et géométrie

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This survey reviews some facts about nonnegativity conditions on the curvature tensor of a Riemannian manifold which are preserved by the action of the Ricci flow. The text focuses on two main points. First we describe the known examples of preserved curvature conditions and how they have been used to derive geometric results, in particular sphere theorems. We then describe some recent results which give restrictions on general preserved conditions. ...

Torsional rigidity on compact Riemannian manifolds with lower Ricci curvature bounds

Najoua Gamara, Abdelhalim Hasnaoui, Akrem Makni (2015)

Open Mathematics

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In this article we prove a reverse Hölder inequality for the fundamental eigenfunction of the Dirichlet problem on domains of a compact Riemannian manifold with lower Ricci curvature bounds. We also prove an isoperimetric inequality for the torsional ridigity of such domains