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- Title
The Riemannian quantitative isoperimetric inequality.
- Authors
Chodosh, Otis; Engelstein, Max; Spolaor, Luca
- Abstract
We study the Riemannian quantitive isoperimetric inequality. We show that a direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed Riemannian manifold. In spite of this, we show that the inequality is true generically. Moreover, we show that a modified (but sharp) version of the quantitative isoperimetric inequality holds for a real analytic metric, using the Łojasiewicz-Simon inequality. The main novelty of our work is that in all our results we do not require any a priori knowledge on the structure/shape of the minimizers.
- Subjects
RIEMANNIAN geometry; MATHEMATICAL equivalence; EUCLIDEAN geometry; MACHINE learning; DEEP learning
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2023, Vol 25, Issue 5, p1711
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1223