Mappings with subexponentially integrable distortion: Modulus of continuity, and distortion of Hausdorff measure and Minkowski content

Abstract

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.