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Abstract In this paper we study the prescribed centroaffine curvature problem in the Euclidean space R n + 1 . This problem is equivalent to solving a Monge–Ampere equation on… Click to show full abstract
Abstract In this paper we study the prescribed centroaffine curvature problem in the Euclidean space R n + 1 . This problem is equivalent to solving a Monge–Ampere equation on the unit sphere. It corresponds to the critical case of the Blaschke–Santalo 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.
Keywords:
priori estimates;
estimates existence;
centroaffine curvature;
prescribed centroaffine;
problem;
curvature problem
Journal Title: Journal of Functional Analysis
Year Published: 2018
Link to full text (if available)
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Journal Title: Journal of Functional Analysis
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!