arXiv subjects
Publications and source records attributed to Aleksandra Zapadinskaya.
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.
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.
We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is essentially sharp in the plane.