We consider solutions to the equation detD2φ=μ when μ has a doubling property. We prove new geometric characterizations for this doubling property (by means of the so-called engulfing property) and deduce the quantitative ...

In this article we prove a theorem on the size of the image of sections of a convex function under its normal mapping when the sections satisfy a geometric property. We apply this result to get new geometric characterizations ...

An important question about a. ne skeletons is the existence of differential equations that are related to the 'affine distance' and the 'area distance' (hence to a. ne skeletons) in the same way the Eikonal equation is ...

Se demuestra una estimacion a priori de las segundas derivadas de una solucion de la ecuacion linearizada de Monge-Ampere.

We prove a mean value inequality for non-negative solutions to L in any domain Ω∈∈ n , where L is the Monge-Ampère operator linearized at a convex function, under minimal assumptions on the Monge-Ampère measure of. An ...

We consider convex solutions to the Monge-Ampere equation when the measure is doubling.We summarized the latest results on geometric and measure theoretic properties associatesto the solutions. We also discuss applications ...

In a previous paper, it was proved that the area based affine distance of a convex region in the plane satisfies a non-homogeneous Monge-Ampere differential equation. Based on this equation, in this paper we propose a fast ...

A special case of the problem of Minkowski on hypersurfaces of space type in Rn;1 is discussed which translates in terms of differential equations to solve an equation of Monge-Ampére type, are simplified such equation ...

There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic ...

Neste trabalho ilustramos a aplicação do Método de "Shooting" em duas classes totalmente distintas de problemas de Equações Diferenciais parciais - ambas com valores de fronteira nulos e em domínios limitados -, uma ...