2014/01/07 by Vicent Gimeno, Gimeno, Vicent, Steen Markvorsen +1
Mathematics · #53C #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A #math.DG #msc:53A #msc:53C
paper · pdf · doi:10.48550/arxiv.1401.1329
21 pages, 1 figure. arXiv admin note: text overlap with arXiv:1104.5417 by other authors
arxiv created 2014/01/07 · arxiv updated 2014/01/08
We study the volume of extrinsic balls and the capacity of extrinsic annuli in minimal submanifolds which are properly immersed with controlled radial sectional curvatures into an ambient manifold with a pole. The key results are concerned with the comparison of those volumes and capacities with the corresponding entities in a rotationally symmetric model manifold. Using the asymptotic behavior of the volumes and capacities we then obtain upper bounds for the number of ends as well as estimates for the fundamental tone of the submanifolds in question.