ON THE MAXIMAL RANK PROBLEM FOR THE COMPLEX HOMOGENEOUS MONGE-AMPERE EQUATION

被引：2
作者：
Ross, Julius [1 ]
Nystrom, David Witt [2 ,3 ]
机构：
[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge, England
[2] Chalmers Univ Technol, Dept Math Sci, Gothenburg, Sweden
[3] Univ Gothenburg, Gothenburg, Sweden
来源：
ANALYSIS & PDE | 2019年 / 12卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
32W20; 35J60; 31C10; 35J70; MICROSCOPIC CONVEXITY PRINCIPLE; ELLIPTIC-EQUATIONS; KAHLER-METRICS; THEOREM; GEOMETRY;
D O I：
10.2140/apde.2019.12.493
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give examples of regular boundary data for the Dirichlet problem for the complex homogeneous Monge-Ampere equation over the unit disc, whose solution is completely degenerate on a nonempty open set and thus fails to have maximal rank.
引用
收藏
页码：493 / 504
页数：12
相关论文
共 22 条
[1]   Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes [J].
Berman, Robert ;
Demailly, Jean-Pierre .
PERSPECTIVES IN ANALYSIS, GEOMETRY, AND TOPOLOGY: ON THE OCCASION OF THE 60TH BIRTHDAY OF OLEG VIRO, 2012, 296 :39-+
[2]   A STRUCTURAL CONDITION FOR MICROSCOPIC CONVEXITY PRINCIPLE [J].
Bian, Baojun ;
Guan, Pengfei .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 28 (02) :789-807
[3]   A microscopic convexity principle for nonlinear partial differential equations [J].
Bian, Baojun ;
Guan, Pengfei .
INVENTIONES MATHEMATICAE, 2009, 177 (02) :307-335
[4]  
Blocki Z., 2009, ADV LECT MATH ALM, V21, P3
[5]   CONVEXITY OF SOLUTIONS OF SEMILINEAR ELLIPTIC-EQUATIONS [J].
CAFFARELLI, LA ;
FRIEDMAN, A .
DUKE MATHEMATICAL JOURNAL, 1985, 52 (02) :431-456
[6]   A constant rank theorem for solutions of fully nonlinear elliptic equations [J].
Caffarelli, Luis ;
Guan, Pengfei ;
Ma, Xi-Nan .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2007, 60 (12) :1769-1791
[7]   Geometry of Kahler metrics and foliations by holomorphic discs [J].
Chen, X. X. ;
Tian, G. .
PUBLICATIONS MATHEMATIQUES, NO 107, 2008, 107 (107) :1-107
[8]  
Chen XX, 2000, J DIFFER GEOM, V56, P189
[9]  
Donaldson SK., 2002, J. Symplectic Geom., V1, P171, DOI 10.4310/JSG.2001.v1.n2.a1
[10]   A maximum rank problem for degenerate elliptic fully nonlinear equations [J].
Guan, Pengfei ;
Phong, D. H. .
MATHEMATISCHE ANNALEN, 2012, 354 (01) :147-169
123