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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1978-0487726-1
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 $ {N^{1/2}}$ 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