Hypersurfaces with Prescribed $lpha$-Relative Gauss-Kronecker Curvature

WU Yadong; ZHAO Guosong

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Hypersurfaces with Prescribed $lpha$-Relative Gauss-Kronecker Curvature

WU Yadong,ZHAO Guosong

Department of Mathematics, Sichuan University, Chengdu 610064

*Correspondence author

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Funding: NSFC （No.11171235）, RFDP （No.201001811100071）

Opened online:31 December 2013

Accepted by: none

Citation: WU Yadong,ZHAO Guosong.Hypersurfaces with Prescribed $lpha$-Relative Gauss-Kronecker Curvature[OL]. [31 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4578330

Considering the $lpha$-relative normalizationon hypersurfaces, we derive the equations of hypersurfaces with$lpha$-relative Gauss-Kronecker curvature. By solving two linkedMonge-Amp$grave{e}$re equations with Dirichlet boundary conditions,we construct hyperbolic hypersurfaces such that their$lpha$-relative Gauss-Kronecker curvature are the given functions.

Keywords:Hyperbolic hyersurface, a-Relative Gauss-Kronecker Curvature, Monge-Ampere PDE

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