Parabolicity and the Liouville Property on Complete Riemannian Manifolds
Parabolicity and the Liouville Property on Complete Riemannian Manifolds
复制标题
完全黎曼流形上的抛物线和刘维尔性质
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
J. Kazdan
中科院分区：
文献类型：
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作者：
J. Kazdan
由于它在许多应用中出现，数学的中心问题之一是理解方程
Because of its appearance in so many applications, one of the central problems in mathematics is to understand the equation
$${ ext{Lu}},{ ext{ = }},Delta { ext{u}},{ ext{ + }},{ ext{a(x)u}},{ ext{ = }},{ ext{f(x)}}$$
(1)
on a Riemannian manifold (M,g) of dimension n. Here a(x) and f(x) are given functions. The simplest questions are the existence and uniqueness of solutions. While they are fairly well understood on a compact manifold M without boundary, and also on a compact manifold with boundary (of course one adds appropriate boundary conditions), there is very little known if (M,g) is complete but not compact.