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Results in Mathematics

, Volume 59, Issue 3–4, pp 545–562 | Cite as

Hyperbolic Relative Hyperspheres with Li-normalization

  • Min XiongEmail author
  • Baoying Yang
Article

Abstract

Consider a graph hypersurface
$$M=\{(x_1,\ldots,x_n,f(x_1,\ldots,x_n))\;\;|\;\; (x_1,\ldots,x_n)\in \Omega\}$$
where f is a strictly convex function defined on a convex domain Ω in real affine space A n . Assume that the hypersurface has a Li-normalization. We study hyperbolic affine hyperspheres with respect to this relative normalization and classify the subclass which is Euclidean complete.

Mathematics Subject Classification (2010)

53A15 35J60 35J65 53C42 58J60 

Keywords

Euclidean completeness classification of hyperbolic Li hyperspheres Monge-Ampère equation 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.College of MathematicsSichuan UniversityChengduPeople’s Republic of China
  2. 2.College of ScienceSouthwest University of Science and TechnologyMianyangPeople’s Republic of China
  3. 3.College of MathematicsSouthwest Jiaotong UniversityChengduPeople’s Republic of China

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