曲线族的模不等式

研究了曲线族的模 ,得到了 :1 )设Γ是 Rn 中连结不相交的曲线α1 与α2 的曲线族 ,若d(α1 ,α2 )≥ r,minj=1 ,2 dia(αj)≤ s,则 M(Γ )≤ 1 +srnΩn. 2 )设Γ是连结 Rn 中的闭连集 F1 与 F2 的曲线族 ,若minj=1 ,2 dia( Fj)≥ ad( F1 ,F2 ) ,则 M( Γ)≥ C( n,a) . 3 )设 R=R( C,C0 )是 R2 中的环 ,D表示 R2 \C中含 R的一个分支 ,α,β是 C上两条不相交的子曲线 .若 ΓR,ΓD 分别是 R与 D中连结 α和 β的曲线族 ,则 M( ΓR)≤ M( ΓD)≤φ( mod R) M(ΓR)

Mudule Inequalities of the Curves Family

This paper study the module of curves family and obtain: 1) Let Γ be the curves family which join the (disjoint) curve α_1 and α_2 in (R)~n, if d(α_1,α_2)≥r, minj=1,2dia(α_j)≤s, then M(Γ)≤1+sr~nΩ_n. 2) Let Γ be the curves (family) which join the continum F_1 and F_2, if minj=1,2dia(F_j)≥ad(F_1,F_2), then M(Γ)≥C(n,a). 3) Let R=R(C,C_0) be a ring in ((R))~2, denotes D be a component of ((R))~2\C which contain R, α、βC are two disjoint subcurves. If Γ_R and Γ_D are the curves which join α_1 and α_2 in R and D respectively, then M(Γ_R)≤M(Γ_D)≤φ(modR)M(Γ_R).