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Smooth solutions to the Christoffel–Minkowski problem in hyperbolic space

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  15 September 2025

Yating Lei ,
Lu Xu  and
Yutian Zhou
Yating Lei
Affiliation:
School of Mathematics, Hunan University , Changsha 410082, Hunan Province, P.R. China. e-mail: leiyating@hnu.edu.cn zhouyutian@hnu.edu.cn
Lu Xu*
Affiliation:
School of Mathematics, Hunan University , Changsha 410082, Hunan Province, P.R. China. e-mail: leiyating@hnu.edu.cn zhouyutian@hnu.edu.cn
Yutian Zhou
Affiliation:
School of Mathematics, Hunan University , Changsha 410082, Hunan Province, P.R. China. e-mail: leiyating@hnu.edu.cn zhouyutian@hnu.edu.cn
*
e-mail: xulu@hnu.edu.cn
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Abstract

In this article, we consider a fully nonlinear equation associated with the Christoffel–Minkowski problem in hyperbolic space. By using the full rank theorem, we establish the existence of h-convex solutions when the prescribed functions on the right-hand side are under some appropriate assumption.

Keywords

h-convex solutionChristoffel–Minkowski problemfull rank theorem

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J15: Second-order elliptic equations 35A01: Existence problems

Information

Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 29
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The authors are supported by NSFC No. 12171143 and NSFC No. 12571214.

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