论文标题
liouville type定理，用于Riemannian歧管之间的几个广义图
Liouville type theorem for several generalized maps between Riemannian manifold
论文作者
论文摘要
在本文中，我们主要使用保护法来得出广义图的单调性公式，包括$ ϕ $ - $ f $谐波映射，以及$ ϕ $ -F $ -F $交响的地图，带有$ M $形式和度量衡量标准的潜在，$ P $ Harmonic Map带有潜在的，$ v $ ankimonic Map，$ v $ aremonic地图。作为推论，我们可以在某些有限的能量孔中得出这些地图的liouville定理。我们还以$ ϕ $ - $ f $谐波映射以及$ ϕ $ - $ f $ - $ f $ symphonic地图在公制测量空间上的渐近conditon下获得了liouville type定理。我们还以$ ϕ $ - $ f $ - $ v $ -V $ -V $ -V $ -V $ -V $ -V $ -V $ -V $ -V $ - harmonic的地图以及公制度量空间上的截面曲率界限。我们还以$ ϕ $ - $ f $ - 谐波的地图获得了liouville定理，而无需在公制测量空间上使用单调公式。
In this paper, we mainly derive monotonicity formula of generalized map using conservation law, including $ϕ$-$F$ harmonic map coupled with $ϕ$-$F$ symphonic map with $m$ form and potential from metric measure space, $ p $ harmonic map with potential , $ V $ harmonic map with potential. As an corollary, we can derive Liouville theorem for these maps under some finite energy conditons. We also get Liouville type theorem for $ϕ$-$F$ harmonic map coupled with $ϕ$-$F$ symphonic map under asymptotic conditon on metric measure space. We also get Liouville theorem for $ϕ$-$F$-$V$-harmonic maps in terms of the upper bound of Ricci curvature and the bound about sectional curvature on metric measure space. We also get Liouville theorem for $ϕ$-$ F $-harmonic map without using monotonicity formula on metric measure space.
