Absolutely area minimizing singular cones of arbitrary codimension

Author:
David Bindschadler

Journal:
Trans. Amer. Math. Soc. **243** (1978), 223-233

MSC:
Primary 49F22; Secondary 58A25

MathSciNet review:
0487726

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Abstract: The examples of area minimizing singular cones of codimension one discovered by Bombieri, DeGiorgi and Guisti are generalized to arbitrary codimension, thus filling a dimensional gap. Previously the only nontrivial examples of singular area minimizing integral currents of codimension other than one were obtained from holomorphic varieties and hence of even codimension. Specifically, let *S* be the *N*-fold Cartesian product of *p*-dimensional spheres and *C* be the cone over *S*. We prove that for *p* sufficiently large, *C* is absolutely area minimizing. It follows from the technique used that *C* restricted to the ball of radius is the unique solution to the oriented Plateau problem with boundary *S*.

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0487726-1

Keywords:
Plateau problem,
integral current,
interior regularity,
area minimizing cones

Article copyright:
© Copyright 1978
American Mathematical Society