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Mean curvature versus diameter and energy quantization

Mean curvature versus diameter and energy quantization We first partially extend a theorem of Topping, on the relation between mean curvature and intrinsic diameter, from immersed submanifolds of Rn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {R}^{n} $$\end{document} 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales mathématiques du Québec Springer Journals

Mean curvature versus diameter and energy quantization

Savelyev, Yasha
Annales mathématiques du Québec , Volume 44 (2) – Oct 18, 2020
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Publisher
Springer Journals
Copyright
Copyright © Fondation Carl-Herz and Springer Nature Switzerland AG 2019
Subject
Mathematics; Mathematics, general; Number Theory; Algebra; Analysis
ISSN
2195-4755
eISSN
2195-4763
DOI
10.1007/s40316-019-00127-0
Publisher site
See Article on Publisher Site

Abstract

We first partially extend a theorem of Topping, on the relation between mean curvature and intrinsic diameter, from immersed submanifolds of Rn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {R}^{n} $$\end{document} 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.

Journal

Annales mathématiques du Québec – Springer Journals

Published: Oct 18, 2020

References

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    Shilnikov, A; Shilnikov, L; Turaev, D
  • Note on trajectories in a solid torus
    Fuller, FB
  • Extended Fuller index, sky catastrophes and the Seifert conjecture
    Savelyev, Yasha
  • Energy quantization and mean value inequalities for nonlinear boundary value problems
    Wehrheim, K
  • Relating diameter and mean curvature for submanifolds of Euclidean space
    Topping, P
  • Geometric Measure Theory
    Federer, Herbert
  • Calibrated geometries
    Harvey, R; Lawson, HB