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.

**[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