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 language | English |
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Article number | 2350055 |
Journal | Communications in Contemporary Mathematics |
Volume | 26 |
Issue number | 10 |
DOIs | |
State | Published - 1 Dec 2024 |
Keywords
- Morse inequalities
- Morse theory
- Persistent homology
- barcode
- calculus of variations
- local connectedness
- minimal surface
- persistent diagram
- q-tameness