关于平移点的刚性

arXiv - MATH - Symplectic Geometry Pub Date : 2024-09-13 DOI:arxiv-2409.08962

Dylan Cant, Jakob Hedicke

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引用次数: 0

摘要

我们证明，存在标准接触球的接触异托邦，其时间-1映射不存在任何平移点，而这些点在谢卢欣-霍弗距离上最接近同一性。这证明了谢卢欣关于具有足够小的谢卢欣-霍弗规范的刘维尔可填充接触流形的接触异顶存在平移点的定理的尖锐性。

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On the rigidity of translated points

We show that there exist contact isotopies of the standard contact sphere whose time-1 maps do not have any translated points which are optimally close to the identity in the Shelukhin-Hofer distance. This proves the sharpness of a theorem of Shelukhin on the existence of translated points for contact isotopies of Liouville fillable contact manifolds with small enough Shelukhin-Hofer norm.

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arXiv - MATH - Symplectic Geometry

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