论文标题
关于最短曲线的分析条件的半代数集的三角剖分
A triangulation of semi-algebraic sets concerning an analytical condition for shortest-length curves
论文作者
论文摘要
本文涉及实际代数和半代数集的分析分层问题。对于惠特尼（Whitney）在1957年的分层，它将真正的代数设置为部分代数歧管\ cite {w}。 1975年，Hironaka在1975年重申了一个真实的代数集是三角测量的，也将其推广到半代数集，遵循Lojasiewicz在1964年对半分析集的三角构造的想法。遵循他们的示例，并想知道几何形状的外观。本文试图提出一个分层，尤其是细胞分解，以使其满足以下分析特性。考虑到实际代数或半代数集中的两个点之间的任何最短曲线，它最多可以有限地相互作用每个单元格（或单纯形）。
This paper concerns an analytical stratification question of real algebraic and semi-algebraic sets. For Whitney's stratification in 1957, it partitions a real algebraic set into partial algebraic manifolds\cite{W}. In 1975 Hironaka reproved that a real algebraic set is triangulable and also generalized it to semi-algebraic sets, following the idea of Lojasiewicz's triangulation of semi-analytic sets in 1964. Following their examples and wondering how geometry looks like locally. this paper tries to come up with a stratification, in particular a cell decomposition, such that it satisfies the following analytical property. Given any shortest curve between two points in a real algebraic or semi-algebraic set, it interacts each cell (or simplex) at most finitely many times.
