On the Support of Minimizers of Causal Variational Principles
On the Support of Minimizers of Causal Variational Principles
复制标题
关于因果变分原理极小化的支持
DOI：
10.1007/s00205-013-0649-1
复制
发表时间：
2010
影响因子：
2.5
通讯作者：
Daniela Schiefeneder
中科院分区：
文献类型：
--
作者：
F. Finster;Daniela Schiefeneder
引入了紧致流形上的一类因果变分原理，并对其进行了数值和解析分析。在一般的假设下证明了极小化测度的支集要么是完全类时的，要么是奇异的，因为它的内部是空的。在圆，球和某些旗流形的例子中，一般结果补充了更详细和明确的分析极小。在球面上，我们得到了与填充问题和Tammes分布的联系。此外，最小行动估计从上和下。
A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty. In the examples of the circle, the sphere and certain flag manifolds, the general results are supplemented by a more detailed and explicit analysis of the minimizers. On the sphere, we get a connection to packing problems and the Tammes distribution. Moreover, the minimal action is estimated from above and below.