Persistent homology for functionals

Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse and Tompkins in a modern and rigorous framework.

Original languageEnglish
Article number2350055
JournalCommunications in Contemporary Mathematics
Volume26
Issue number10
DOIs
StatePublished - 1 Dec 2024

Keywords

  • Morse inequalities
  • Morse theory
  • Persistent homology
  • barcode
  • calculus of variations
  • local connectedness
  • minimal surface
  • persistent diagram
  • q-tameness

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