Geometric properties of the sections of solutions to the Monge-Ampere equation

Citation
Ce. Gutierrez et Qb. Huang, Geometric properties of the sections of solutions to the Monge-Ampere equation, T AM MATH S, 352(9), 2000, pp. 4381-4396
Citations number
10
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
352
Issue
9
Year of publication
2000
Pages
4381 - 4396
Database
ISI
SICI code
0002-9947(2000)352:9<4381:GPOTSO>2.0.ZU;2-G
Abstract
In this paper we establish several geometric properties of the cross sectio ns of generalized solutions phi to the Monge-Ampere equation det D-2 phi = mu, when the measure mu satisfies a doubling property. A main result is a c haracterization of the doubling measures mu in terms of a geometric propert y of the cross sections of phi. This is used to obtain estimates of the sha pe and invariance properties of the cross sections that are valid under app ropriate normalizations.