Some basic theorems on flat G chains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:418

Article

关键词: Geometric measure theory;    Constancy theorem;    Flat G chain;   

DOI  :  10.1016/j.jmaa.2014.04.024

来源: Elsevier

【 摘 要 】

For a complete normed Abelian group G, we show that a flat G chain (respectively, normal flat G chain) of codimension 0 in a finite dimensional Banach space corresponds to a G valued functions that is H-m summable (respectively, of bounded variation). We also prove a constancy theorem for an m dimensional flat G chain T in a metric space assuming supp T is contained in the closure of a connected m dimensional Lipschitz submanifold M with M boolean AND supp partial derivative T = empty set and H-m(M) = H-m(Clos M) < infinity. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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