A classical theorem of Bôcher says a positive harmonic function on a punctured domain \(\mathcal {O}\setminus p\) in Euclidean space can be written as the sum of a constant multiple of the Green function with pole at p and a function harmonic on all of \(\mathcal {O}\). Here we establish such a result in the setting of functions on a Riemannian manifold with rather rough metric tensor.

中文翻译：

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具有粗糙系数的博歇定理

伯歇尔（Bôcher）的一个经典定理说，在欧几里得空间中一个穿孔域\（\ mathcal {O} \ setminus p \）上的正谐波函数可以写成Green函数的常数倍与p在一个极点上对所有\（\ mathcal {O} \）的谐波。在这里，我们在具有相当粗糙的度量张量的黎曼流形上的函数设置中建立了这样的结果。