Saved in:
Bibliographic Details
Main Author: Kang, Jungsoo
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2304.07016
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917125788008448
author Kang, Jungsoo
author_facet Kang, Jungsoo
contents The original Arnold chord conjecture states that every closed Legendrian submanifold of the standard contact sphere $S^{2n-1}$ admits a Reeb chord with distinct endpoints with respect to any contact form. In this paper, we prove this conjecture for contact forms induced by strictly convex embeddings into $\mathbb{R}^{2n}$ under the assumption that minimal periodic Reeb orbits are of Morse-Bott type. We also provide a counterexample when the convexity condition is not satisfied.
format Preprint
id arxiv_https___arxiv_org_abs_2304_07016
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the strong Arnold chord conjecture for convex contact forms
Kang, Jungsoo
Symplectic Geometry
The original Arnold chord conjecture states that every closed Legendrian submanifold of the standard contact sphere $S^{2n-1}$ admits a Reeb chord with distinct endpoints with respect to any contact form. In this paper, we prove this conjecture for contact forms induced by strictly convex embeddings into $\mathbb{R}^{2n}$ under the assumption that minimal periodic Reeb orbits are of Morse-Bott type. We also provide a counterexample when the convexity condition is not satisfied.
title On the strong Arnold chord conjecture for convex contact forms
topic Symplectic Geometry
url https://arxiv.org/abs/2304.07016