Persistent homology for functionals
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
30 December 2023
|
| In: |
Communications in contemporary mathematics
Year: 2023, Volume: 25 |
| ISSN: | 0219-1997 |
| DOI: | 10.1142/S0219199723500554 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S0219199723500554 Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/10.1142/S0219199723500554 
|
| Author Notes: | Ulrich Bauer, Anibal M. Medina-Mardones, and Maximilian Schmahl |
| Summary: | 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. |
|---|---|
| Item Description: | Gesehen am 13.05.2024 |
| Physical Description: | Online Resource |
| ISSN: | 0219-1997 |
| DOI: | 10.1142/S0219199723500554 |