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標題Title: AN OPTIMAL GAP THEOREM
作者Authors: LEI NI
上傳單位Department: 電子工程系
上傳時間Date: 2012-12-8
上傳者Author: 傅俊結
審核單位Department: 電子工程系
審核老師Teacher: 傅俊結
檔案類型Categories: 論文Thesis
關鍵詞Keyword: K ̈ahler manifolds
摘要Abstract: By solving the Cauchy problem for the Hodge-Laplace heat equation for d-closed, positive (1,1)-forms, we prove an optimal gap theorem for K ̈ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius r centered at any fixed point o is a function of o(r−2). Furthermore via a relative monotonicity estimate we obtain a
stronger statement, namely a ‘positive mass’ type result, asserting that if (M, g) is not r2 􏰇
flat, then lim infr→∞ Vo(r) Bo(r) S(y) dμ(y) > 0 for any o ∈ M.

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2012_12_5bf96021.pdf 283Kb pdf 121 17
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