sobolev embedding theorem
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2017 ◽  
Vol 60 (4) ◽  
pp. 831-857 ◽  
Author(s):  
Mihai Băileşteanu ◽  
Hung Tran

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.


2017 ◽  
Vol 38 (1) ◽  
pp. 235-252 ◽  
Author(s):  
Sagun Chanillo ◽  
Jean Van Schaftingen ◽  
Po-Lam Yung

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