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Transactions of the American Mathematical Society

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

 

 

A regularity theorem for minimizing hypersurfaces modulo $ \nu$


Author: Frank Morgan
Journal: Trans. Amer. Math. Soc. 297 (1986), 243-253
MSC: Primary 49F22; Secondary 53A10
DOI: https://doi.org/10.1090/S0002-9947-1986-0849477-5
MathSciNet review: 849477
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Abstract: It is proved that an $ (n - 1)$-dimensional, area-minimizing flat chain modulo $ \nu $ in $ {{\mathbf{R}}^n}$, with smooth extremal boundary of at most $ \nu /2$ components, has an interior singular set of Hausdorff dimension at most $ n - 8$. Similar results hold for more general integrands.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0849477-5
Keywords: Area-minimizing, flat chain modulo $ \nu $, regularity
Article copyright: © Copyright 1986 American Mathematical Society