AI 中文总结
介绍曲率有下界的亚历山德罗夫空间，涵盖比较条件、全球化定理等多主题，简述二维理论，为现代亚历山德罗夫几何的主要前身，对该领域相关内容进行了全面介绍。
AI 中文摘要
本文介绍了曲率有下界的亚历山德罗夫空间，涵盖各种比较条件、全球化定理、切空间与方向空间、梯度流、分裂定理、维度与体积、格罗莫夫选择定理、边界与加倍定理以及商空间等主题。还简要概述了二维理论，它是现代亚历山德罗夫几何的主要前身。
英文摘要
An introduction to Alexandrov spaces with curvature bounded below. Topics include various comparison conditions, the globalization theorem, tangent spaces and spaces of directions, gradient flows, the splitting theorem, dimension and volume, Gromov's selection theorem, the boundary and the doubling theorem, and quotient spaces. We also give a brief overview of the two-dimensional theory, the main precursor to modern Alexandrov geometry.
Comments161 pages, 29 figures
