Exception Sets of Intrinsic and Piecewise Lipschitz Functions

Gunther Leobacher, Alexander Steinicke

Research output: Contribution to journalArticleResearchpeer-review


We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their exception sets where the Lipschitz property fails. The newly introduced notion of permeability describes sets which are natural exceptions for Lipschitz continuity in a well-defined sense. One of the main results states that continuous functions which are intrinsically Lipschitz continuous outside a permeable set are Lipschitz continuous on the whole domain with respect to the intrinsic metric. We provide examples of permeable sets in R d, which include Lipschitz submanifolds.

Original languageEnglish
Article number118
Number of pages19
JournalThe journal of geometric analysis
Issue number4
Early online date1 Feb 2022
Publication statusPublished - Apr 2022

Bibliographical note

Publisher Copyright: © 2022, The Author(s).


  • Intrinsic metric
  • Permeable sets
  • Piecewise Lipschitz continuity

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