scholarly journals Some curvature pinching results for Riemannian manifolds with density

2015 ◽  
Vol 144 (2) ◽  
pp. 823-836 ◽  
Author(s):  
William Wylie
Keyword(s):  
Riemannian Manifolds ◽  
Curvature Pinching

scholarly journals A Global Curvature Pinching Result of the First Eigenvalue of the Laplacian on Riemannian Manifolds

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Peihe Wang ◽  
Ying Li
Keyword(s):  
Lower Bound ◽  
Riemannian Manifolds ◽  
Negative Curvature ◽  
First Eigenvalue ◽  
Moser Iteration ◽  
The First Eigenvalue ◽  
Global Curvature ◽  
Sobolev Constant ◽  
Curvature Pinching

The paper starts with a discussion involving the Sobolev constant on geodesic balls and then follows with a derivation of a lower bound for the first eigenvalue of the Laplacian on manifolds with small negative curvature. The derivation involves Moser iteration.

On the equicontinuity of families of inverse mappings of Riemannian manifolds

2019 ◽  
Vol 16 (4) ◽  
pp. 557-566
Author(s):  
Denis Ilyutko ◽  
Evgenii Sevost'yanov
Keyword(s):  
Riemannian Manifolds ◽  
Type Inequality ◽  
The Given ◽  
Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

Ball-homogeneous and disk-homogeneous Riemannian manifolds

1982 ◽  
Vol 180 (4) ◽  
pp. 429-444 ◽  
Author(s):  
Old?ich Kowalski ◽  
Lieven Vanhecke
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds
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