Calculus of Variations and Geometric Measure Theory
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E. Stepanov

Rectifiability of metric flat chains and fractional masses

created by stepanov on 16 Nov 2007
modified on 11 Oct 2010


Published Paper

Inserted: 16 nov 2007
Last Updated: 11 oct 2010

Journal: J. Math. Sciences (N.Y.)
Volume: 167
Number: 3
Pages: 406-417
Year: 2010

(preprint 2007)


It is proven that every real flat chain $T$ of finite mass in a metric space $E$, the density character of which is Ulam number (in particular, in a separable metric space), is rectifiable when $*M*^\alpha(T)<+\infty$ for some $\alpha\in [0,1)$, where $*M*^\alpha(T)$ stands for the $\alpha$-mass of $T$.

Keywords: flat chain, fractional mass, $\alpha$-mass, metric current


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