Asymptotic expansions of complete K\"ahler-Einstein metrics with finite volume on quasi-projective manifolds
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🧮 math.DG
keywords
ahler-einsteinasymptoticcompleteformulamanifoldsquasi-projectivebandocheng-yau
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We give an elementary proof to the asymptotic expansion formula of Rochon-Zhang for the unique complete K\"ahler-Einstein metric of Cheng-Yau, Kobayashi, Tian-Yau and Bando on quasi-projective manifolds. The main tools are the solution formula for second order ODE's with constant coefficients and spectral theory for Laplacian operator on a closed manifold.
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