pinching and compactness theorems for compact riemannian manifolds
Deane Yang (1987-1988)
Séminaire de théorie spectrale et géométrie
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Deane Yang (1987-1988)
Séminaire de théorie spectrale et géométrie
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Mikhael Gromov, H. Blaine Lawson (1983)
Publications Mathématiques de l'IHÉS
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Luis Guijarro, Peter Petersen (1997)
Annales scientifiques de l'École Normale Supérieure
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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
Isaac Chavel, Edgar A. Feldman (1974)
Compositio Mathematica
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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 , which are not locally homogeneous, in general.
Nicolescu, Liviu, Pripoae, Gabriel (1999)
Balkan Journal of Geometry and its Applications (BJGA)
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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,...