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標題Title: Hypersurfaces in Hyperbolic Space with Support Function
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: support function
摘要Abstract: We develop a global correspondence between immersed horospherically convex hy- persurfaces φ : Mn → Hn+1 and complete conformal metrics e2ρgSn on domains Ω in the boundary Sn at infinity of Hn+1, where ρ is the horospherical support function, ∂∞φ(Mn)=∂Ω,andΩistheimageoftheGaussmapG:Mn →Sn.Todosowefirst establish results on when the Gauss map G : Mn → Sn is injective. We also discuss when an immersed horospherically convex hypersurface can be unfolded along the normal flow into an embedded one. These results allow us to establish general Alexandrov reflection principles for elliptic problems of both immersed hypersurfaces in Hn+1 and conformal metrics on domains in Sn. Consequently, we are able to obtain, for instance, a strong Bern- stein theorem for a complete, immersed, horospherically convex hypersurface in Hn+1 of constant mean curvature.

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