Potential Analysis

, Volume 42, Issue 4, pp 749–774 | Cite as

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

  • Vicent Gimeno
  • Steen Markvorsen


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.


First Dirichlet eigenvalue Capacity Effective resistance Minimal submanifolds Fundamental tone Minimal submanifolds 

Mathematics Subject Classification (2010)

53A 53C 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mathematics-INIT-IMACUniversitat Jaume ICastelló de la PlanaSpain
  2. 2.DTU ComputeTechnical University of DenmarkLyngbyDenmark

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