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

Qiu, Hongbing

doi:10.1090/proc/13332

The heat flow of $V$-harmonic maps from complete manifolds into regular balls
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Proc. Amer. Math. Soc. 145 (2017), 2271-2280 Request permission

Abstract:

In this paper, we establish gradient estimates for the heat flow of $V$-harmonic maps from complete noncompact manifolds into regular balls. We also derive a Liouville theorem for $V$-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 $V$-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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