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arXiv · 2209.13892

Some results on the weighted Yamabe problem with or without boundary

Pak Tung Ho·Jinwoo Shin·Zetian Yan
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Abstract

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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Pak Tung Ho, Jinwoo Shin, Zetian Yan. 2022-09-28. Some results on the weighted Yamabe problem with or without boundary. https://arxiv.org/abs/2209.13892

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