On the volume growth and the topology of complete minimal submanifolds of a Euclidean space
Vol. 2 (1995), No. 3, Page 657--669.
Chen, Qing
On the volume growth and the topology of complete minimal submanifolds of a Euclidean space
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Abstract:
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 $k=\sup{\roman{volume}(M\cap B(t)) \over Ï_nt^n}$, where $B(t)$ is the ball of the Euclidean space of center 0 and radius $t$, $Ï_n$ 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.
Mathematics Subject Classification (1991): Primary 49Q05, 53C42; Secondary 53C20, 26B15, 49Q15
Mathematical Reviews Number: MR1382525
Received: 1994-12-08
