Weyl type bounds for harmonic functions
Weyl type bounds for harmonic functions
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DOI：
10.1007/s002220050204
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发表时间：
1998-02
影响因子：
3.1
通讯作者：
T. Colding;William P. Minicozzi II
中科院分区：
文献类型：
--
作者：
T. Colding;William P. Minicozzi II
The purpose of this paper is to give sharp polynomial bounds in the order of growth for the dimension of the space of harmonic functions with a fixed degree of polynomial growth on an open manifold which has a scale invariant Neumann Poincare inequality and in addition either has the doubling property or has the relative volume comparison property. Moreover, we describe an asymptotic formula and an uniform estimate on the remainder for harmonic functions with polynomial growth on open manifolds with nonnegative Ricci curvature. This formula strongly resembles the Weyl asymptotic formula for eigenfunctions on compact domains in Euclidean space. In fact this new asymptotic formula contains a significant part of the
