2022-09-25T23:17:59Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000403422021-03-01T21:01:05ZOn the volume growth and the topology of complete minimal submanifolds of a Euclidean spaceChen, Qing138940415application/pdfLet $M$ 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 paperGraduate School of Mathematical Sciences, The University of Tokyo1995application/pdfJournal of mathematical sciences, the University of Tokyo32657669AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40342/files/jms020307.pdfeng