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A class of prescribed shifted Gauss curvature equations for horo-convex hypersurfaces in $ \mathbb{H}^{n+1} $

  • * Corresponding author: Qiang Tu

    * Corresponding author: Qiang Tu

The first author is supported by Natural Science Foundation of Hubei Province, China, No. 2020CFB246

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  • Inspired by the generalized Christoffel problem, we consider a class of prescribed shifted Gauss curvature equations for horo-convex hypersurfaces in $ \mathbb{H}^{n+1} $. Under some sufficient conditions, we prove the a priori estimates for solutions to the Monge-Ampère type equation $ \det(\kappa-\mathbf{1}) = f(X, \nu(X)) $. Moreover, we obtain an existence result for the compact horo-convex hypersurface $ M $ satisfying the above equation with various assumptions.

    Mathematics Subject Classification: Primary: 35J96, 53C45; Secondary: 53A05.


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