Skip navigation
Skip navigation

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

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

Description

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
URI: http://hdl.handle.net/1885/139100
Source: Journal of Functional Analysis
DOI: 10.1016/j.jfa.2017.08.024

Download

File Description SizeFormat Image
1-s2.0-S0022123617303385-main.pdf436.49 kBAdobe PDFThumbnail
    Request a copy


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  12 November 2018/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator