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http://dx.doi.org/10.4134/BKMS.b181181

A MONOTONICITY FORMULA AND A LIOUVILLE TYPE THEOREM OF V-HARMONIC MAPS  

Zhao, Guangwen (School of Mathematical Sciences Fudan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.5, 2019 , pp. 1327-1340 More about this Journal
Abstract
We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.
Keywords
V-harmonic map; monotonicity formula; Liouville type theorem; holomorphic map; constant boundary-value problem;
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