Calculus of Variations and Geometric Measure Theory

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