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標題Title: HYPERSURFACES IN HYPERBOLIC POINCARE ́ MANIFOLDS AND CONFORMALLY INVARIANT PDES
作者Authors: VINCENT BONINI JOSE ́ M. ESPINAR AND JIE QING
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: eigenvalue
摘要Abstract: WederivearelationshipbetweentheeigenvaluesoftheWeyl- Schouten tensor of a conformal representative of the conformal infinity of a hyperbolic Poincar ́e manifold and the principal curvatures on the level sets of its uniquely associated defining function with calculations based on [9] [10]. This relationship generalizes the result for hypersurfaces in Hn+1 and their connection to the conformal geometry of Sn as exhibited in [7] and gives a correspondence between Weingarten hypersurfaces in hyperbolic Poincar ́e manifolds and conformally invariant equations on the conformal infinity. In particular, we generalize an equivalence exhibited in [7] between Christoffel-type problems for hypersurfaces in Hn+1 and scalar curvature problems on the conformal infinity Sn to hyperbolic Poincar ́e manifolds.

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2012_12_bd2669e6.pdf 192Kb pdf 118 18
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