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

被引：53

作者：

Gutiérrez, CE ^{[1
]}

Huang, QB ^{[1
]}

机构：

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 352卷 / 09期

关键词：

real Monge-Ampere equation; Aleksandrov's solutions; doubling measures; strict convexity; spaces of homogenous type;

D O I：

10.1090/S0002-9947-00-02491-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we establish several geometric properties of the cross sections 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 characterization of the doubling measures mu in terms of a geometric property of the cross sections of phi. This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.

引用

页码：4381 / 4396

页数：16

共 10 条

[1] Balls and quasi-metrics: A space of homogeneous type modeling the real analysis related to the Monge-Ampere equation [J].