scholarly journals Dissipative Numerical Schemes on Riemannian Manifolds with Applications to Gradient Flows

2018 ◽  
Vol 40 (6) ◽  
pp. A3789-A3806 ◽  
Author(s):  
Elena Celledoni ◽  
Sølve Eidnes ◽  
Brynjulf Owren ◽  
Torbjørn Ringholm
Keyword(s):  
Riemannian Manifolds ◽  
Gradient Flows ◽  
Numerical Schemes

Spectral analysis of Morse-Smale gradient flows

2019 ◽  
Vol 52 (6) ◽  
pp. 1403-1458
Author(s):  
Nguyen Viet DANG ◽  
Gabriel RIVIERE
Keyword(s):  
Spectral Analysis ◽  
Gradient Flows

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.

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