scholarly journals The integrable harmonic map problem versus Ricci flow

2012 ◽  
Vol 865 (2) ◽  
pp. 308-329 ◽  
Author(s):  
Sergei L. Lukyanov
Keyword(s):  
Ricci Flow ◽  
Harmonic Map ◽  
Problem Versus

scholarly journals On the stability of harmonic maps under the homogeneous Ricci flow

2018 ◽  
Vol 5 (1) ◽  
pp. 122-132
Author(s):  
Rafaela F. do Prado ◽  
Lino Grama
Keyword(s):  
Ricci Flow ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
The Stability

Abstract In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow.We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow does not preserve the stability of an harmonic map.

scholarly journals Heat Kernel Estimates Under the Ricci–Harmonic Map Flow

2017 ◽  
Vol 60 (4) ◽  
pp. 831-857 ◽  
Author(s):  
Mihai Băileşteanu ◽  
Hung Tran
Keyword(s):  
Ricci Flow ◽  
Harmonic Map ◽  
Embedding Theorem ◽  
Sobolev Embedding ◽  
Sobolev Embedding Theorem ◽  
Kernel Estimates ◽  
Best Constant ◽  
Entropy Functional ◽  
Conjugate Heat Equation ◽  
Harmonic Map Flow

AbstractThis paper considers the Ricci flow coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat equation and we prove an analogue of Perelman's differential Harnack inequality. As an application, we find a connection between the entropy functional and the best constant in the Sobolev embedding theorem in ℝn.

scholarly journals Gradient estimates for the heat equation under the Ricci-harmonic map flow

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Mihai Bailesteanu
Keyword(s):  
Heat Equation ◽  
Positive Solutions ◽  
Ricci Flow ◽  
Harmonic Map ◽  
Gradient Estimates ◽  
Complete Manifold ◽  
Harnack Inequalities ◽  
Harmonic Map Flow

AbstractThe paper establishes a series of gradient estimates for positive solutions to the heat equation on a manifold M evolving under the Ricci flow, coupled with the harmonic map flow between M and a second manifold N. We prove Li-Yau type Harnack inequalities and we consider the cases when M is a complete manifold without boundary and when M is compact without boundary.

scholarly journals Results on coupled Ricci and harmonic map flows

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Michael Bradford Williams
Keyword(s):  
Ricci Flow ◽  
Principal Bundle ◽  
Harmonic Map ◽  
Geometric Flow ◽  
Geometric Context ◽  
Special Case ◽  
Harmonic Map Flow

Abstract We explore the harmonic-Ricci flow - that is, Ricci flow coupled with harmonic map flow - both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate that one natural geometric context for the flow is a special case of the locally ℝ

Conditions to extend the Ricci flow coupled with harmonic map flow

2017 ◽  
Vol 28 (12) ◽  
pp. 1750091
Author(s):  
Jun Sun
Keyword(s):  
Ricci Flow ◽  
Harmonic Map ◽  
Integral Conditions ◽  
Harmonic Map Flow

In this paper, we provide some integral conditions to extend the Ricci flow coupled with harmonic map flow. Our results generalize the corresponding results for Ricci flow obtained by Wang [On the conditions to extend Ricci flow, Int. Math. Res. Not. 8 (2008), Articles: rnn012, 30 pp].

Ricci Flow on Quasi Einstein Manifold

2010 ◽  
Vol 0 (-1) ◽  
pp. 447-454
Author(s):  
A. Bhattacharyya ◽  
T. De
Keyword(s):  
Ricci Flow ◽  
Einstein Manifold
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