A priori estimates and existence of solutions to the prescribed centroaffine curvature problem
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.
|Collections||ANU Research Publications|
|Source:||Journal of Functional Analysis|
|Access Rights:||Open Access|
|1-s2.0-S0022123617303385-main.pdf||436.49 kB||Adobe PDF|
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