2023-10-02T14:11:41Z
https://repository.dl.itc.u-tokyo.ac.jp/oai
oai:repository.dl.itc.u-tokyo.ac.jp:00040342
2022-12-19T04:15:42Z
312:6865:7063:7064
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On the volume growth and the topology of complete minimal submanifolds of a Euclidean space
Chen, Qing
138940
415
application/pdf
Let $M$ be a $n$-dimensional complete properly immersed minimal submanifold of a Euclidean space. We show that the number of the ends of $M$ is bounded above by $k=\sup{\roman{volume}(M\cap B(t)) \over ω_nt^n}$, where $B(t)$ is the ball of the Euclidean space of center 0 and radius $t$, $ω_n$ is the volume of $n$-dimensional unit Euclidean ball. Moreover, we prove that the number of ends of $M$ is equal to $k$ under some curvature decay condition.
departmental bulletin paper
Graduate School of Mathematical Sciences, The University of Tokyo
1995
application/pdf
Journal of mathematical sciences, the University of Tokyo
3
2
657
669
AA11021653
13405705
https://repository.dl.itc.u-tokyo.ac.jp/record/40342/files/jms020307.pdf
eng