一般 Hirsch问题(英文)

On General Hirsch Problem

Hirsch问题 :设 U R3,V R2 为开集 ,如果 f∶ U→ V是 C1满映射 ,则 f必须有正则点吗 ?更一般地 ,张敦穆 [8]提出了一般的 Hirsch问题 :设 N ,P为 Cm 流形 ,dim N =n,dimp =p,n >p,f∶ N→ P是 Cr映射 ( 1≤ r≤ n) .当 1≤ r≤ n -p时 f必须有正则点吗 ?本文讨论了这个问题 ,应用 [8]中方法和 Norton[5]和 Bates[1 ]的估计 ,我们得到了定理 1和定理 2 .它们部分地推广了

The Hirsch Problem (HP) asked : Let UR3,VR2 be open sets. If f∶U→V is C 1 and surjective, must f have regular points? More generally, Zhang proposed a General Hirsch Problem (GHP): Let N,P be Cm manifolds, dim N=n,dimP=p,n>p,f∶N→P is Cr map(1≤r≤m). When 1≤r≤n-p, must f have regular points? We discuss this problem. Using the method in and an estimated due to Norton and Bates , we get Theorem 1 an d Theorem 2. They partially generalize the main theorem in .