Abstract
In this paper we establish several geometric properties of the cross sections of generalized solutions ϕ \phi to the Monge-Ampère equation det D 2 ϕ = μ \det D^{2}\phi = \mu , when the measure μ \mu satisfies a doubling property. A main result is a characterization of the doubling measures μ \mu in terms of a geometric property of the cross sections of ϕ \phi . This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
