# Some Results on the Weighted Yamabe Problem with or Without Boundary

@article{Ho2022SomeRO, title={Some Results on the Weighted Yamabe Problem with or Without Boundary}, author={Pak Tung Ho and Jin‐Hyuk Shin and Zetian Yan}, journal={SSRN Electronic Journal}, year={2022} }

Let $(M^n,g,e^{-\phi}dV_g,e^{-\phi}dA_g,m)$ be a compact smooth metric measure space with boundary with $n\geqslant 3$. In this article, we consider several Yamabe-type problems on a compact smooth metric measure space with or without boundary: uniqueness problem on the weighted Yamabe problem with boundary, characterization of the weighted Yamabe solitons with boundary and the existence of positive minimizers in the weighted Escobar quotient.

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