Rectifiability; a survey

Abstract

This is a survey on rectifiability. I discuss basic properties of rectifiable sets, measures, currents and varifolds and their role in complex and harmonic analysis, potential theory, calculus of variations, PDEs and some other topics.

129 pages, several small changes and additions

References in corpus (4)

• Boundedness of the square function and rectifiability
• C^1 Hypersurfaces of the Heisenberg Group are N-Rectifiable
• Geometric conditions for the $L^2$-boundedness of singular integral operators with odd kernels with respect to measures with polynomial growth in ${\mathbb{R}}^d$
• Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds