Mean Value Inequalities

نویسندگان

  • Peter Li
  • Jiaping Wang
  • PETER LI
  • JIAPING WANG
چکیده

In this article, we will discuss various issues concerning when a complete Riemannian manifold possesses a global mean value inequality for positive subsolutions of either the Laplace equation or the heat equation. This study is motivated by the recent result of the first author [L1]. In that paper, he proved estimates on the dimensions of spaces of harmonic functions of at most polynomial growth of degree d on manifolds satisfying the weak volume growth condition and the mean value inequality . Let us first recall the weak volume growth condition.

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تاریخ انتشار 2007