In this talk, based in a joint work with Steen Markvorsen, I will tread to explore the relation between capacity, the volume growth, the finiteness of the number of ends and asymptotic planes of minimal submanifolds properly immersed into ambient manifolds with a pole and bounded radial curvatures. We will show upper and lower bounds for the number of ends in terms of the volume growth, in the line of [3,1] and finally, using the finiteness of the volume growth we will provide an upper bound for the capacity of an extrinsic annulus in terms of the volume growth that can be understood as a reverse of the results of [2].

[1] V. Gimeno and V. Palmer. Volume growth, number of ends, and the topology of a complete submanifold, Journal of Geometric Analysis (2012), 1-22.

[2] S. Markvorsen and V. Palmer. Transience and capacity of minimal submanifolds, Geom. Funct. Anal. 13 (2003), no. 4, 915-933. MR 2006562 (2005d:58064).

[3] V.G. Tkachev. Finiteness of the number of ends of minimal submanifolds in Euclidean space, Manuscripta Math. 82 (1994), no. 3-4, 313-330. MR 1265003 (95h:53012).