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arXiv · 1908.00677

The Riemannian Quantitative Isoperimetric Inequality

Otis Chodosh·Max Engelstein·Luca Spolaor
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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 structure/shape of the minimizers.

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Otis Chodosh, Max Engelstein, Luca Spolaor. 2019-08-02. The Riemannian Quantitative Isoperimetric Inequality. https://arxiv.org/abs/1908.00677

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