CC-p调和映照的Liouville型定理

Liouville Type Theorem for CC-p Harmonic Maps

拟调和映照以及广义拟调和映照在研究拟Hermitian几何中发挥着重要作用。在前期工作的基础上,考虑引入p-水平能量泛函以及相应的p-水平应力能量张量,此张量成为研究守恒律的有利工具并且推导出与该张量联系紧密的基本积分公式。利用此基本积分公式建立关于p-水平能量张量的单调不等式,推导出关于p-水平能量增长性条件下CC-p调和映照的Liouville型定理。此类型的Liouville型定理有助于进一步理解与拟Hermitian流形相关的性质。

The theory of pseudoharmonic and general pseudoharmonic maps plays an important role in studying pseudo-Hermitian geometry.In spired by the previous work,p-horizontal energy and p-horizontal stress-energy tensor have been introduced.This stressenergytensor becomes a useful tool to investigate theconservation law of CC-p harmonic maps and the basic integral formulae.Usingthe basic integral formulae,one can establish some monotonicity formulae for CC-p harmonic maps.Liouville type results follow immediatelyfrom these monotonicity formulae and the basic integral formulae under suitable growth conditions on the p-horizontal energy.These results become a useful tool to investigate the properties of pseudo-Hermitian geometry.