Whitney extension theorem and intrinsic rectifiability of jump sets in Carnot-Carathéodory spaces

Abstract

We prove that the intrinsic jump set of every locally integrable function on an equiregular Carnot-Carathéodory space is intrinsically countably rectifiable. A key new ingredient is a local scalar Whitney extension theorem for intrinsic $C^1$ functions.

arXiv comment23 pages