Undistorted fillings in subsets of metric spaces

Lipschitz k-connectivity, Euclidean isoperimetric inequalities, and coning inequalities all measure the difficulty of filling a k-dimensional cycle in space by (k+1)-dimensional object. In many cases, such as Banach spaces CAT(0) spaces, it is easy to prove connectivity or inequality, but harder obtain inequality. We show that finite Nagata dimension, connectedness implies imply inequalities. this proving if X has dimension k-connected admits up k then any isometric embedding into metric isoperimetrically undistorted k+1. Since embeds L∞, which inequality well. addition, we an analog Federer-Fleming deformation theorem holds use k-connected, integral (k+1)-currents can be approximated chains total mass.