Zygmund微分映射的正则点

该文的主要结果是: 对任意Zygmund类$C^{p,Z}$映射$f:R^{n}\rightarrow R^{m}$, 若$\frac{n-m}{2}\leq p\leq n-m-1$, 则有mes$K_{f}>0$或者mes$C_{f}>0$. 这个结果给出了Hirsch问题的部分回答.

On the Regular Points of Zygmund Differentiable Maps

The main result of this article is: For any Zygmund class $C^{p,Z}$map $f:R^{n}\rightarrow R^{m}$ if $\frac{n-m}{2}\leq p\leq n-m-1$, then either mes$K_{f}>0$ or mes$C_{f}>0$. It provides a partial answer of the Hirsch Problem.