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Aug 11, 2021 at 15:04 comment added memorial In the non-compact case, nothing of this nature works.
Aug 8, 2021 at 12:29 comment added geometricK Just to clarify, does this apply if $M$ is an open submanifold of a closed manifold? (I guess this should be similar to the case of a compact manifold with boundary with the Dirichlet boundary condition $f=0$ on the boundary.)
Aug 7, 2021 at 1:54 vote accept geometricK
Aug 5, 2021 at 13:06 history edited memorial CC BY-SA 4.0
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Aug 5, 2021 at 12:59 history edited memorial CC BY-SA 4.0
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Aug 5, 2021 at 12:54 history edited memorial CC BY-SA 4.0
added material
Aug 5, 2021 at 12:46 history answered memorial CC BY-SA 4.0