A Gromov's dimension comparison estimate for rectifiable sets
Valentino Magnani, Aleksandra Zapadinskaya
TL;DR
This paper extends Gromov's dimension comparison estimate to rectifiable sets from Sobolev mappings, using weak exterior differentiation and a new low rank property for Sobolev maps.
Contribution
It introduces a novel extension of Gromov's estimate to rectifiable sets via Sobolev mappings, employing weak exterior differentiation and low rank properties.
Findings
Gromov's dimension estimate applies to a broader class of rectifiable sets.
Development of a weak exterior differentiation framework for pullback forms.
Identification of a low rank property for Sobolev mappings.
Abstract
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.
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