Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A MONOTONICITY FORMULA AND A LIOUVILLE TYPE THEOREM OF V-HARMONIC MAPS

  • Received : 2018.12.04
  • Accepted : 2019.03.08
  • Published : 2019.09.30
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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.

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References

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