Some results on the weighted Yamabe problem with or without boundary

초록

Let (Mn, g, e-phi dVg, e-phi dAg, m) be a compact smooth metric measure space with boundary with n 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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