淡江大學機構典藏:Item 987654321/125097
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    题名: Deformation of the weighted scalar curvature
    作者: Ho, Pak tung
    关键词: weighted scalar curvature;smooth metric measure space;vacuum static space
    日期: 2023-11-04
    上传时间: 2024-03-01 12:05:29 (UTC+8)
    摘要: 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 L2ϕ
    -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.
    關聯: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 19,　087
    DOI: 10.3842/SIGMA.2023.087
    显示于类别:[應用數學與數據科學學系] 期刊論文

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