scholarly journals Ricci flow coupled with harmonic map flow

2012 ◽  
Vol 45 (1) ◽  
pp. 101-142 ◽  
Author(s):  
Reto Müller
Keyword(s):  
Ricci Flow ◽  
Harmonic Map ◽  
Harmonic Map Flow

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].

Infinite time blow-up for half-harmonic map flow from R into S1

2021 ◽  
Vol 143 (4) ◽  
pp. 1261-1335
Author(s):  
Yannick Sire ◽  
Juncheng Wei ◽  
Youquan Zheng
Keyword(s):  
Blow Up ◽  
Harmonic Map ◽  
Infinite Time ◽  
Harmonic Map Flow

scholarly journals Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
James Kohout ◽  
Melanie Rupflin ◽  
Peter M. Topping
Keyword(s):  
Constant Curvature ◽  
Harmonic Map ◽  
Gradient Flow ◽  
Minimal Immersion ◽  
Curvature Surface ◽  
Previous Theory ◽  
Target Manifold ◽  
Harmonic Map Flow

AbstractThe harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as {t\to\infty}.

scholarly journals Moving mesh for the axisymmetric harmonic map flow

2005 ◽  
Vol 39 (4) ◽  
pp. 781-796
Author(s):  
Benoit Merlet ◽  
Morgan Pierre
Keyword(s):  
Harmonic Map ◽  
Moving Mesh ◽  
Harmonic Map Flow

scholarly journals Asymptotics of the Teichmüller harmonic map flow

2013 ◽  
Vol 244 ◽  
pp. 874-893 ◽  
Author(s):  
Melanie Rupflin ◽  
Peter M. Topping ◽  
Miaomiao Zhu
Keyword(s):  
Harmonic Map ◽  
Harmonic Map Flow
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