闭半代数集的欧拉示性数和Lipschitz-Killing曲率

Euler阻塞和Lipschitz-Killing曲率

Euler obstruction and Lipschitz-Killing curvatures

将闭次解析集的局部Gauss-Bonnet公式应用于复解析情形，得到了复解析芽的Euler阻塞的Lipschitz-Killing曲率和正则部分的Chern形式的特征.我们还证明了类似的结果为全球欧拉障碍。作为推论，我们肯定地回答了傅立叶关于Euler阻塞和Gauss-Bonnet测度的一个问题。

Whitney分层与局部Lipschitz Killing曲率的连续性

Whitney stratifications and the continuity of local Lipschitz Killing curvatures

证明了多项式有界的o-极小结构中可定义集的局部Lipschitz Killing曲率沿Whitney分层和局部Lipschitz分层是连续的，如果这些分层是（w）-正则的.

Lipschitz-Killing曲率与极像

Lipschitz-Killing curvatures and polar images

我们涉及的Lipschitz-Killing措施的可定义的集合$X \subset \mathbb{R}^n$在一个O-最小结构的通用极像的体积。对于$\mathbb{R}^n$的光滑子流形，Langevin和Shifrin建立了这样的结果，然后我们给出了这些结果的无穷小形式。作为推论，我们得到了孔德和梅尔的极不变量和一般极像的密度之间的关系。

Equi-singularity of real families and Lipschitz Killing curvature densities at infinity

Fix an o-minimal structure expanding the ordered field of real numbers. Let $(W_y)_{y\in\mathbb{R}^s}$ be a definable family of closed subsets of $\mathbb{R}^n$ whose total space $W = \cup_y W_y\times y$ is a closed connected $C^2$ definable sub-manifold of $\mathbb{R}^n\times\mathbb{R}^s$. Let $φ:W \to\mathbb{R}^s$ be the restriction of the projection to the second factor. After defining $K(φ)$, the set of generalized critical values of $φ$, showing that they are closed and definable of positive codimension in $\mathbb{R}^s$, contain the bifurcation values of $φ$ and are stable under generic …

双 Lipschitz 不变量在奇点理论中的应用：Lojasiewicz 指数和欧拉阻挠

Bi-Lipschitz Invariants in Singularity Theory: Lojasiewicz Exponent and Euler Obstruction

本文研究了奇点理论中两个基本局部不变量的双 Lipschitz 不变性，即 Lojasiewicz 指数和局部欧拉阻挠，探讨了其在双 Lipschitz 等价下的保持条件，并回答了局部欧拉阻挠是否为双 Lipschitz 不变量的问题。