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Deformation of the Weighted Scalar Curvature
Pak Tung Hoa, Jinwoo Shinb a Department of Mathematics, Tamkang University, Tamsui, New Taipei City 251301, Taiwan
b Korea Institute for Advanced Study, Hoegiro 85, Seoul 02455, Korea
Abstract:
Inspired by the work of Fischer–Marsden [Duke Math. J. 42 (1975), 519–547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal $L_\phi^2$-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particular, we define a weighted vacuum static space, and study locally conformally flat weighted vacuum static spaces. We then prove some stability results of the weighted scalar curvature on flat spaces. Finally, we consider the prescribed weighted scalar curvature problem on closed smooth metric measure spaces.
Keywords:
weighted scalar curvature, smooth metric measure space, vacuum static space.
Received: December 7, 2022; in final form October 30, 2023; Published online November 4, 2023
Citation:
Pak Tung Ho, Jinwoo Shin, “Deformation of the Weighted Scalar Curvature”, SIGMA, 19 (2023), 087, 15 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1982 https://www.mathnet.ru/eng/sigma/v19/p87
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Abstract page: | 28 | Full-text PDF : | 4 | References: | 7 |
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