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Ends, Fundamental Tones, and Capacities of Minimal Submanifolds Via Extrinsic Comparison Theory

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...

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Bibliographic Details
Published in:Potential analysis 2015-05, Vol.42 (4), p.749-774
Main Authors: Gimeno, Vicent, Markvorsen, Steen
Format: Article
Language:English
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Summary: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.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-014-9456-z