Calculus of Variations and Geometric Measure Theory

V. Magnani - A. Zapadinskaya

A Gromov's dimension comparison estimate for rectifiable sets

created by magnani on 23 Jul 2015
modified on 12 Jun 2017


Published Paper

Inserted: 23 jul 2015
Last Updated: 12 jun 2017

Journal: Selecta Math. (N.S.)
Volume: 23
Number: 2
Pages: 1153-1174
Year: 2017


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.

Tags: GeMeThNES
Keywords: Hausdorff dimension, Sobolev mapping, hypersurface, rectifiable set, sub-Riemannian distance, nilpotent Lie group, exterior differentiation