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A priori estimates and existence of solutions to the prescribed centroaffine curvature problem

Jian, Huaiyu; Lu, Jian; Wang, Xu-Jia


In this paper we study the prescribed centroaffine curvature problem in the Euclidean space Rⁿ⁺¹. This problem is equivalent to solving a Monge–Ampère equation on the unit sphere. It corresponds to the critical case of the Blaschke–Santaló inequality. By approximation from the subcritical case, and using an obstruction condition and a blow-up analysis, we obtain sufficient conditions for the a priori estimates, and the existence of solutions up to a Lagrange multiplier.

CollectionsANU Research Publications
Date published: 2018
Type: Journal article
Source: Journal of Functional Analysis
DOI: 10.1016/j.jfa.2017.08.024
Access Rights: Open Access


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