Global smoothing of a subanalytic set

全局子解析弧对称集

Globally subanalytic arc-symmetric sets

研究证明了全局子解析弧对称集可由连续全局子解析函数表示，该函数在简单正常交集外具有弧解析性质。

次解析函数收敛半径与扩张半径的控制

Control of radii of convergence and extension of subanalytic functions

设g表示欧几里得空间的开子集U上的实解析函数，S表示U的边界点，其中g不允许局部解析扩张.我们证明了，如果g是半代数的（分别，全球次解析的），那么S是半代数的（分别，次解析的）和g扩展到一个社区的cl（U）§作为一个解析函数，是半代数的（分别，全球次解析的）。(In在一般的次解析情形下，S不一定是次解析的）。我们的证明依赖于控制的收敛半径的幂级数G集中在点的图像中的解析映射，在收敛半径的拉回G在点的源。

Uniform parameterization of subanalytic sets and diophantine applications

We prove new parameterization theorems for sets definable in the structure $\mathbb{R}_{an}$ (i.e. for globally subanalytic sets) which are uniform for definable families of such sets. We treat both $C^r$-parameterization and (mild) analytic parameterization. In the former case we establish a polynomial (in $r$) bound (depending only on the given family) for the number of parameterizing functions. However, since uniformity is impossible in the latter case (as was shown by Yomdin via a very simple family of algebraic sets), we introduce a new notion, analytic quasi-parameterization (where many-…