关于Heins端的椭圆维数

On Elliptic Dimensions On Heins Ends

考虑镶边Ｒｉｅｍａｎｎ曲面＝Ω∪Ω，其边界Ω由有限条互不相交的解析Ｊｏｒｄａｎ曲线组成．设Ｐ是Ω上的有限密度．又设Ω的理想边界β的调和测度为零，且由有限个Ｓｔｏｉｌｏｗ边界点｛δ＿１，…，δ＿Ｋ｝组成若每个δ＿ｉ满足Ｎ＿ｉ阶广义Ｈｅｉｎｓ条件，则Ω的椭圆维数不超过（Ｎ＿ｉ＋１）－１．

Consider a noncompact bordered Riemann surface Ω=Ω∪ with com-pact border and null ideal boundary. Let P be a non-negative locally Holder continuouscovariant bivector on Ω and P∈L(Ω). By discussing the solutions of the equations △u=Puand ,where e_p is the P-unit solution of △u=Pu,it is proved that foran end Ω with a finite number K of ideal boundary elements in the sense of Kerekjato-Stoilow,if each boundary point δ_i satisfies so called N_i-Heins conditions,then the elliptic di-mention of Ω is not greater than.