High-Dimensional Fillings in Heisenberg Groups

Research output: Contribution to journalArticlepeer-review


We use intersections with horizontal manifolds to show that high-dimensional cycles in the Heisenberg group can be approximated efficiently by simplicial cycles. This lets us calculate all of the higher-order Dehn functions of the Heisenberg groups, thus proving a conjecture of Gromov.

Original languageEnglish (US)
Pages (from-to)1596-1616
Number of pages21
JournalJournal of Geometric Analysis
Issue number2
StatePublished - Apr 1 2016


  • Carnot geometry
  • Dehn functions
  • Filling inequalities
  • Heisenberg group
  • Sub-Riemannian geometry

ASJC Scopus subject areas

  • Geometry and Topology


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