Pointwise differentiability of higher order for sets

Ulrich Menne*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that differentials are Borel functions, higher-order rectifiability of the set of differentiability points, and a Rademacher result. One concept is characterised by a limit procedure involving inhomogeneously dilated sets. The original motivation to formulate the concepts stems from studying the support of stationary integral varifolds. In particular, strong pointwise differentiability of every positive integer order is shown at almost all points of the intersection of the support with a given plane.

Original languageEnglish
Pages (from-to)591-621
Number of pages31
JournalAnnals of Global Analysis and Geometry
Issue number3
Publication statusPublished - 2019 Apr 1


  • Higher-order pointwise differentiability
  • Rademacher–Stepanov type theorem
  • Rectifiability
  • Stationary integral varifold

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology


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