一个托波诺戈夫的全球化结果为洛伦兹长度空间
Tobias Beran1, John Harvey2, Lewis Napper3
1Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria.
概括
这项研究引入了一个新的全球化定理 洛伦兹长度空间与时间的曲率边界,利用一个新的"猫猫.
科学领域:
- 不同几何学微分几何学
- 一般相对论一般相对论.
- 尺度几何几何学 尺度几何学
背景情况:
- 洛伦兹长度空间是洛伦兹多样性的概括.
- 曲率界限对于理解这些空间的几何学是至关重要的.
- 托波诺戈夫的全球化定理是里曼几何学的基本结果.
研究的目的:
- 为洛伦兹长度空间提供托波诺戈夫的全球化定理的合成模拟.
- 为了扩展罗伦斯几何学中关于曲率极限的结果.
- 探索广义相对论和几何分析中的应用.
主要方法:
- 使用一个使用一个.
- Meta_Description='探索一个新的全球化定理,用于具有时间形曲率边界的洛伦兹长度空间,在几何学和相对论中有应用.
主要成果:
- 托波诺戈夫的全球化定理的合成类比,用于具有较低时间形曲率边界的洛伦兹长度空间.
- 一个关于三角形子划分的定理和一个合成的洛伦斯式莱贝斯格数定理.
- 时间函数和零距离在全球过度的洛伦兹长度空间上的属性.
结论:
- 提出的结果将古典几何定理扩展到合成的洛伦兹设置.
- 应用程序包括波内特-迈尔斯和分割定理的版本.
- 讨论了格罗莫夫-豪斯多夫收下曲率极限的稳定性.
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