The heat flow of 𝑉-harmonic maps from complete manifolds into regular balls

Qiu, Hongbing

doi:10.1090/proc/13332

The heat flow of -harmonic maps from complete manifolds into regular balls

Author: Hongbing Qiu
Journal: Proc. Amer. Math. Soc. 145 (2017), 2271-2280
MSC (2010): Primary 58E20, 53C43
DOI: https://doi.org/10.1090/proc/13332
Published electronically: January 27, 2017
MathSciNet review: 3611336
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Abstract: In this paper, we establish gradient estimates for the heat flow of -harmonic maps from complete noncompact manifolds into regular balls. We also derive a Liouville theorem for -harmonic maps, which improves Theorem 2 in a prior work of the author, Chen and Jost and covers the results of that work and a work of Brighton. Furthermore, using these gradient estimates, we prove the global existence for the -harmonic map heat flow and generalize the result obtained by Chen-Jost-Wang to the case where the domain manifold is complete noncompact.

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