Nodal domains and growth of harmonic functions on noncompact manifolds
Nodal domains and growth of harmonic functions on noncompact manifolds
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DOI：
10.1007/bf02921335
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
H. Donnelly;C. Fefferman
中科院分区：
文献类型：
--
作者：
H. Donnelly;C. Fefferman
研究完备黎曼流形上的调和函数。给出了变符号有界调和函数的衰减估计。对于变号无界调和函数，得到了增长性与节点域之间的关系。在非负Ricci曲率的黎曼流形上，人们猜想，至多具有给定多项式增长级的调和函数一定构成有限维向量空间。这个猜想在某些特殊情况下成立。
Harmonic functions are studied on complete Riemannian manifolds. A decay estimate is given for bounded harmonic functions of variable sign. For unbounded harmonic functions of variable sign, relations are derived between growth properties and nodal domains. On Riemannian manifolds of nonnegative Ricci curvature, it has been conjectured that harmonic functions, having at most a given order of polynomial growth, must form a finite dimensional vector space. This conjecture is established in certain special cases.