Calculus of Variations and Geometric Measure Theory
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O. Chodosh - M. Engelstein - L. Spolaor

The Riemannian quantitative isoperimetric inequality

created by spolaor on 03 Oct 2019

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Submitted Paper

Inserted: 3 oct 2019
Last Updated: 3 oct 2019

Year: 2019

Abstract:

We study the Riemannian quantiative isoperimetric inequality. We show that 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 Lojasiewicz-Simon inequality. A main novelty of our work is that in all our results we do not require any a priori knowledge on the structureshape of the minimizers.


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