RECTIFIABILITY OF FLAT CHAINS IN BANACH SPACES WITH COEFFICIENTS IN Zp
نویسندگان
چکیده
Aim of this paper is a finer analysis of the group of flat chains with coefficients in Zp introduced in [7], by taking quotients of the group of integer rectifiable currents, along the lines of [27, 15]. We investigate the typical questions of the theory of currents, namely rectifiability of the measure-theoretic support and boundary rectifiability. Our main result can also be interpreted as a closure theorem for the class of integer rectifiable currents with respect to a (much) weaker convergence, induced by flat distance mod(p), and with respect to weaker mass bounds. A crucial tool in many proofs is the isoperimetric inequality proved in [7] with universal constants. In order to illustrate our results we start with a few basic definitions. Let us denote by Ik(E) the class of integer rectifiable currents with finite mass in a metric space E and let us given for granted the concepts of boundary ∂, mass M, push-forward in the more general context of currents (see [4] and the short appendix of [7]). We denote by Fk(E) the currents that can by written as R + ∂S with R ∈ Ik(E) and S ∈ Ik+1(E). It is obviously an additive Abelian group and
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