Abstract
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.
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Work partially supported by NSF grant DMS-1500817.
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Taylor, M. Bôcher’s Theorem with Rough Coefficients. Potential Anal 56, 65–86 (2022). https://doi.org/10.1007/s11118-020-09876-y
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DOI: https://doi.org/10.1007/s11118-020-09876-y