Applications of Fixed Point Theorems to the Vacuum Einstein Constraint Equations with Non-Constant Mean Curvature

被引：5

作者：

The Cang Nguyen ^{[1
]}

机构：

[1] Univ Tours, UFR Sci & Tech, Lab Math & Phys Theor, Parc Grandmont, F-37200 Tours, France

来源：

ANNALES HENRI POINCARE | 2016年 / 17卷 / 08期

关键词：

Point Theorem; Constraint Equation; Vector Equation; Limit Equation; Nonempty Compact Convex Subset;

D O I：

10.1007/s00023-015-0446-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem), while the second one uses the concept of half-continuity coupled with the introduction of local supersolutions. These methods allow to: unify some recent existence results, simplify many proofs (for instance, the one of the main theorems in Dahl et al., Duke Math J 161(14):2669-2697, 2012) and weaken the assumptions of many recent results.

引用

页码：2237 / 2263

页数：27

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