Abstract
<p style='text-indent:20px;'>Inspired by the generalized Christoffel problem, we consider a class of prescribed shifted Gauss curvature equations for horo-convex hypersurfaces in <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{H}^{n+1} $\end{document}</tex-math></inline-formula>. Under some sufficient conditions, we prove the a priori estimates for solutions to the Monge-Ampère type equation <inline-formula><tex-math id="M3">\begin{document}$ \det(\kappa-\mathbf{1}) = f(X, \nu(X)) $\end{document}</tex-math></inline-formula>. Moreover, we obtain an existence result for the compact horo-convex hypersurface <inline-formula><tex-math id="M4">\begin{document}$ M $\end{document}</tex-math></inline-formula> satisfying the above equation with various assumptions.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference23 articles.
1. S. B. Alexander, R. J. Currier.Nonnegatively curved hypersurfaces of hyperbolic space and subharmonic functions, J. London Math. Soc., 41 (1990), 347-360.
2. I. Ja. Bakel'man, B. E. Kantor.Existence of a hypersurface homeomorphic to the sphere in Euclidean space with a given mean curvature, Geometry and Topology, 1 (1974), 3-10.
3. L. Caffarelli, L. Nirenberg, J. Spruck.The Dirichlet problem for nonlinear second order elliptic equations. I. Monge-Ampère equation, Comm. Pure Appl. Math., 37 (1984), 369-402.
4. L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second order elliptic equations, IV. Starshaped compact Weingarten hypersurfaces, Current Topics in Partial Differential Equations, (1986), 1–26.
5. F. J. de Andrade, J. L. M. Barbosa, J. H. S. de Lira.Closed Weingarten hypersurfaces in warped product manifolds, Indiana Univ. Math. J., 58 (2009), 1691-1718.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献