REGULAR DOMAINS AND SURFACES OF CONSTANT GAUSSIAN CURVATURE IN 3-DIMENSIONAL AFFINE SPACE

被引：3
|
作者：
Nie, Xin [1 ]
Seppi, Andrea [2 ,3 ]
机构：
[1] Southeast Univ, Shing Tung Yau Ctr, Nanjing, Peoples R China
[2] CNRS, Gieres, France
[3] Univ Grenoble Alpes, Gieres, France
来源：
ANALYSIS & PDE | 2022年 / 15卷 / 03期
关键词：
domain of dependence; affine differential geometry; affine Gauss-Kronecker curvature; Monge-Ampere equation; MINKOWSKI PROBLEM; HYPERSURFACES;
D O I：
10.2140/apde.2022.15.643
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Generalizing the notion of domains of dependence in the Minkowski space, we define and study regular domains in the affine space with respect to a proper convex cone. In three dimensions, we show that every proper regular domain is uniquely foliated by some particular surfaces with constant affine Gaussian curvature. The result is based on the analysis of a Monge-Ampere equation with extended real-valued lower semicontinuous boundary condition.
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页码：643 / 697
页数：55
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