系数为$Z_p$的巴拿赫空间中平坦链的可求正性
Rectifiability of flat chains in Banach spaces with coefficients in $Z_p$
摘要：
本文的目的是一个更精细的分析组的系数在$Z_p$在最近的一篇论文中介绍了Ambrosio-Katz，通过采取组的整数可整流电流，沿线的Ziemer和Federer的方法。我们研究了电流理论的典型问题，即测量理论支持的可校正性和边界可校正性。我们的主要结果也可以被解释为封闭定理的一类整数整流电流相对于一个（更）弱的收敛，诱导平坦的距离模$p$，并相对于较弱的质量边界。Ambrosio-Katz用普适常数证明的等周不等式是许多证明的重要工具。
英文摘要：
Aim of this paper is a finer analysis of the group of flat chains with coefficients in $Z_p$ introduced in a recent paper by Ambrosio-Katz, by taking quotients of the group of integer rectifiable currents, along the lines of the the Ziemer and Federer approach. 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 by Ambrosio-Katz with universal constants.
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