The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 370–377 | Cite as

A Criterion for Uniqueness of Tangent Cones at Infinity for Minimal Surfaces

  • Paul GallagherEmail author


We partially resolve a conjecture of Meeks on the asymptotic behavior of minimal surfaces in \(\mathbb {R}^3\) with quadratic area growth.


Differential geometry Minimal surfaces Geometric analysis Tangent cones Uniqueness Scherk 

Mathematics Subject Classification

49Q05 53A10 



The author would like to thank his advisor, William Minicozzi, as well as Jonathan Zhu, Frank Morgan, Ao Sun, and Nick Strehlke for their comments and suggestions throughout the writing of this paper. Many thanks also to the referee’s helpful suggestions.


  1. 1.
    Colding, T.H., II, W.P.M.: A Course in Minimal Surfaces. American Mathematical Society, Providence, RI (2011)CrossRefzbMATHGoogle Scholar
  2. 2.
    Collin, P.: Topologie et courbure des surfaces minimales proprement plonges de \(\mathbb{R}^3\). Ann. Math 145(2), 1–31 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Meeks III, W.H.: Global problems in classical minimal surface theory. In: Hoffman, D. (ed.) Global Theory of Minimal Surfaces, pp. 453–470. American Mathematical Society, Providence, RI (2005)Google Scholar
  4. 4.
    Meeks III, W.H., Wolf, M.: Minimal surfaces with the area growth of two planes: the case of infinite symmetry. J. AMS 20(2), 441–465 (2006)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Schoen, R.: Uniqueness, symmetry, and embeddedness of minimal surfaces. JDG 18, 791–809 (1983)MathSciNetzbMATHGoogle Scholar
  6. 6.
    White, B.: Tangent cones to two-dimensional area-minimizing integral currents are unique. Duke Math. J. 50(1), 143–160 (1983)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations