کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665292 1633808 2015 43 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Hypersurfaces in hyperbolic space with support function
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Hypersurfaces in hyperbolic space with support function
چکیده انگلیسی

Based on [19], we develop a global correspondence between immersed hypersurfaces ϕ:Mn→Hn+1ϕ:Mn→Hn+1 satisfying an exterior horosphere condition, also called here horospherically concave hypersurfaces, and complete conformal metrics e2ρgSne2ρgSn on domains Ω in the boundary SnSn at infinity of Hn+1Hn+1, where ρ   is the horospherical support function, ∂∞ϕ(Mn)=∂Ω∂∞ϕ(Mn)=∂Ω, and Ω is the image of the Gauss map G:Mn→SnG:Mn→Sn. To do so we first establish results on when the Gauss map G:Mn→SnG:Mn→Sn is injective. We also discuss when an immersed horospherically concave 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+1Hn+1 and conformal metrics on domains in SnSn. Consequently, we are able to obtain, for instance, a strong Bernstein theorem for a complete, immersed, horospherically concave hypersurface in Hn+1Hn+1 of constant mean curvature.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 280, 6 August 2015, Pages 506–548
نویسندگان
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