Abstract
In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {f n } from long cylinders P n with \(\int_{P_n } {|A_{f_n } |^2 } + \mu (f_n (P_n )) < \Lambda \). We show that if {f n } does not converge to a point, the total Gauss curvatures and the measures of the images of {f n } will not lose on the necks and each neck consists of a point.
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Supported by National Natural Science Foundation of China (Grant No. 11201131)
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Chen, L. On the convergence behavior of conformal immersion sequence from cylinders. Acta. Math. Sin.-English Ser. 30, 1050–1060 (2014). https://doi.org/10.1007/s10114-014-1614-0
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DOI: https://doi.org/10.1007/s10114-014-1614-0