We study mappings of finite distortion whose distortion functions are locally subexponentially integrable. We establish a local modulus of continuity estimate for the inverse of such a map. As applications, we describe the possible expansion and compression of certain Hausdorff measures and Minkowski contents under such mappings. We also exhibit examples that describe the extent to which our results are sharp.
"Mappings with subexponentially integrable distortion: Modulus of continuity, and distortion of Hausdorff measure and Minkowski content." Illinois J. Math. 57 (4) 965 - 1008, Winter 2013. https://doi.org/10.1215/ijm/1417442558