On the preservation of eccentricities of monge–ampère sections

Abstract

A study on the preservation of eccentricities of Monge–Ampère sections under an integral Dini-type condition on the Monge–Ampère measure is presented. The approach is based solely on C2, α-estimates for solutions to the Monge–Ampère equation. The main results are then related to the local quasi-conformal Jacobian problem and to a priori estimates for solutions to the linearized Monge–Ampère equation.