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標題Title: ON POSITIVE SOLUTIONS TO SEMI-LINEAR CONFORMALLY INVARIANT EQUATIONS ON LOCALLY CONFORMALLY FLAT MANIFOLDS
作者Authors: Jie Qing and David Raske
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: yamabe
摘要Abstract: In this paper we study the existence and compactness of positive solu-
tions to a family of conformally invariant equations on closed locally conformally flat
manifolds. The family of conformally covariant operators Pα were introduced via the
scattering theory for Poincar ́e metrics associated with a conformal manifold (M n , [g]).
We prove that, on a closed and locally conformally flat manifold with Poincar ́e ex-
ponent less than n−α for some α ∈ [2, n), the set of positive smooth solutions to the
equation
2
n+α Pαu = un−α
is compact in the C∞ topology. Therefore the existence of positive solutions follows from the existence of Yamabe metrics and a degree theory.

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2012_12_f2b573c0.pdf 188Kb pdf 103 14
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