In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {fn} from long cylinders Pn with Pn｜Afn｜2＋ μ（fn（Pn）） 〈 Λ. We show that if {fn} does not converge to a point...In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {fn} from long cylinders Pn with Pn｜Afn｜2＋ μ（fn（Pn）） 〈 Λ. We show that if {fn} does not converge to a point, the total Gauss curvatures and the measures of the images of {fn} will not lose on the necks and each neck consists of a point.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11201131)
文摘In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {fn} from long cylinders Pn with Pn｜Afn｜2＋ μ（fn（Pn）） 〈 Λ. We show that if {fn} does not converge to a point, the total Gauss curvatures and the measures of the images of {fn} will not lose on the necks and each neck consists of a point.
