A monotonicity formula and a Liouville type theorem of $V$-harmonic maps
Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1327-1340
https://doi.org/10.4134/BKMS.b181181
Published online September 30, 2019
Guangwen Zhao
Fudan University
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
MSC numbers : Primary 58E20, 53C43, 35B53, 53C55
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