التفاصيل البيبلوغرافية
| العنوان: |
Persistent homology for functionals. |
| المؤلفون: |
Bauer, Ulrich, Medina-Mardones, Anibal M., Schmahl, Maximilian |
| المصدر: |
Communications in Contemporary Mathematics; Dec2024, Vol. 26 Issue 10, p1-40, 40p |
| مصطلحات موضوعية: |
MINIMAL surfaces, CALCULUS of variations, MORSE theory, HOMOLOGY theory, FUNCTIONALS |
| مستخلص: |
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. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |