n维拟共形映照的Mori（型）不等式的加强

STRENGTHENED FORMS OF MORI’S AND MORI-TYPETHEOREMS IN N-DIMENSIONAL QUASICONFORMAL MAPPINGS

设ｆ是ｎ维空间Ｒ￣ｎ的单位球到自身上的Ｋ—拟共形映照且ｆ（０）＝０．记又设ｙ＿ｋ∈ｌ＿ｋ∩ｆ（γ＿ｋ）（γ））且适合｜ｙ＿ｋ｜＝ｍａｘ｛｜ｙ｜；∈ｌ＿ｋ∩ｆ（γ＿Ｋ（γ））｝．本文证明了：而且，当ｎ＝２时，上式成为等式。此处，η＿ｍ为仅与ｎ、ｍ有关的常数（详见正文中的（８）式）．

Suppose that f is a K-quasiconformal mapping of the unit ball onto itself with the originfixed.Set and And suppose that y_k is the point in l_k∩f(γ_K(r))with|y_k|=max{|y|;y∈l_k∩f(γ_K))}.Inthis paper,the following main result is obtained:supdepending on n and m.The equality holds with