中文摘要：

设（M，g）是带度量g的n维黎曼流形，p（x）〉1是M上的C^1光滑函数，本文证明了在一定的体积增长的条件下，M上关于变指数Laplace算子div（｜ u｜……p（x）-2 ）的弱极大值原理，并利用该极大值原理证明了相应于变指数Laplace算子的Liouville型定理．

英文摘要：

noncompact volume was Laplace was A weak maximum principle for the variable exponent Laplace on a complete Riemannian manifold under suitable conditions about the growth of the established, by which a Liouville type theorem for the variable exponent proved.