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Finite groups and invariant solutions to one-dimensional Plateau problems


Author: David Bindschadler
Journal: Proc. Amer. Math. Soc. 80 (1980), 621-626
MSC: Primary 49F22; Secondary 53A10
DOI: https://doi.org/10.1090/S0002-9939-1980-0587939-9
MathSciNet review: 587939
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Abstract | References | Similar Articles | Additional Information

Abstract: Let G be a finite group of isometries acting on a complete Riemannian manifold. Suppose that B is a 0-dimensional boundary which is G-invariant. If the order of G divides the product of the cardinality of the orbit and the density of B at each point, then a G-invariant absolutely length minimizing integral current with boundary B can be constructed.


References [Enhancements On Off] (What's this?)

  • [B] D. E. Bindschadler, Invariant solutions to the oriented Plateau problem of maximal codimension, Trans. Amer. Math. Soc. 261 (1980), 439-462. MR 580897 (81k:49032)
  • [BJ] J. E. Brothers, Invariance of solutions to invariant parametric variational problems, Trans. Amer. Math. Soc. 262 (1980), 159-179. MR 583850 (82h:49027)
  • [F1] H. Federer, Geometric measure theory, Springer-Verlag, New York, 1969. MR 0257325 (41:1976)
  • [F2] -, Real flat chains, cochains and variational problems, Indiana Univ. Math. J. 24 (1974), 351-407. MR 0348598 (50:1095)
  • [L] H. B. Lawson, The equivariant Plateau problem and interior regularity, Trans. Amer. Math. Soc. 173 (1973), 231-249. MR 0308905 (46:8017)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0587939-9
Keywords: Plateau problem, area minimizing, integral current, invariant solution
Article copyright: © Copyright 1980 American Mathematical Society

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