Generalized Dimension Distortion under Mappings of Sub-Exponentially Integrable Distortion

We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane

Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of $\mathbb{R}^n$ affect the sizes of the images of sets of Hausdorff dimension less than $n$. We measure the sizes of the image sets in terms of generalized Hausdorff measures

Generalized dimension estimates for images of porous sets under monotone Sobolev mappings

We give an essentially sharp estimate in terms of generalized Hausdorff measures for images of porous sets under monotone Sobolev mappings, satisfying suitable Orlicz-Sobolev conditions

A Gromov's dimension comparison estimate for rectifiable sets

We extend the validity of a Gromov’s dimension comparison estimate for topological hypersurfaces to sufficiently large classes of rectifiable sets, arising from Sobolev mappings. Our tools are a suitably weak exterior differentiation for pullback differential forms and a new low rank property for Sobolev mappings

Regularity and modulus of continuity of space-filling curves

We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example.peerReviewe