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- W2031793297 abstract "The purpose of this paper is to provide a new proof of Bando–Mabuchi’s uniqueness theorem of Kähler Einstein metrics on Fano manifolds, based on the convexity of Ding-functional on Chen’s weak $${mathcal {C}}^{1,bar{1}}$$ geodesic without using any further regularities. Unlike the smooth case, the lack of regularities on the geodesic forbids us to use Futaki’s spectral formula of the weighed Laplacian operator directly. However, we can use smooth $$epsilon $$ -geodesics to approximate the weak one, then prove that a sequence of eigenfunctions will converge into the first eigenspace of the weighted Laplacian operator." @default.
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- W2031793297 date "2014-12-14" @default.
- W2031793297 modified "2023-10-15" @default.
- W2031793297 title "On the spectrum of weighted Laplacian operator and its application to uniqueness of Kähler Einstein metrics" @default.
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- W2031793297 doi "https://doi.org/10.1007/s00208-014-1152-1" @default.
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