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arXiv · 0903.0169

Finiteness of the number of ends of minimal submanifolds in euclidean space

Vladimir G. Tkachev
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Abstract

We prove a version of the well-known Denjoy-Ahlfors theorem about the number of asymptotic values of an entire function for properly immersed minimal surfaces of arbitrary codimension in R^N. The finiteness of the number of ends is proved for minimal submanifolds with finite projective volume. We show, as a corollary, that a minimal surface of codimensionn meeting any n-plane passing through the origin in at most k points has no more c(n,N)k ends.

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Vladimir G. Tkachev. 2009-03-01. Finiteness of the number of ends of minimal submanifolds in euclidean space. https://doi.org/10.1007/bf02567704

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