Inserted: 23 jul 2015
Last Updated: 12 jun 2017
Journal: Selecta Math. (N.S.)
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.
Keywords: Hausdorff dimension, Sobolev mapping, hypersurface, rectifiable set, sub-Riemannian distance, nilpotent Lie group, exterior differentiation