Area-minimizing integral currents with boundaries invariant under polar actions

Author:
Julian C. Lander

Journal:
Trans. Amer. Math. Soc. **307** (1988), 419-429

MSC:
Primary 49F20; Secondary 53A10, 58E15

MathSciNet review:
936826

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Abstract: Let be a compact, connected subgroup of acting on , and let the action of be polar. (Polar actions include the adjoint action of a Lie group on the tangent space to the symmetric space at the identity coset.) Let be an -dimensional submanifold without boundary, invariant under the action of , and lying in the union of the principal orbits of . It is shown that, if is an area-minimizing integral current with boundary , then is invariant under the action of . This result is extended to a larger class of boundaries, and to a class of parametric integrands including the area integrand.

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DOI:
https://doi.org/10.1090/S0002-9947-1988-0936826-4

Article copyright:
© Copyright 1988
American Mathematical Society