Mean curvature versus diameter and energy quantization

Yasha Savelyev

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arXiv · 1902.01834

Mean curvature versus diameter and energy quantization

Yasha Savelyev

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Abstract

We first partially extend a theorem of Topping, on the relation between mean curvature and intrinsic diameter, from immersed submanifolds of $\mathbb{R} ^{n} $ to almost everywhere immersed, closed submanifolds of a compact Riemannian manifold. We use this to prove quantization of energy for pseudo-holomorphic closed curves, of all genus, in a compact locally conformally symplectic manifold.

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Yasha Savelyev. 2019-02-05. Mean curvature versus diameter and energy quantization. https://arxiv.org/abs/1902.01834

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