关于Zoll接触形式的局部辛最优性
辛几何
2023-12-15 v3
摘要
我们证明了接近Zoll接触形式的接触形式的正则形式，并推得任意闭流形上的Zoll接触形式是辛比（systolic ratio）的局部极大化子。该结果的推论有：(i) 针对接近Zoll的Riemannian和Finsler度量的尖锐局部辛不等式，(ii) Viterbo关于凸体辛容量的猜想的扰动情形，(iii) Gromov非挤压定理在中间维度对接近线性辛同胚的推广。
引用
@article{arxiv.1912.04187,
title = {On the local systolic optimality of Zoll contact forms},
author = {Alberto Abbondandolo and Gabriele Benedetti},
journal= {arXiv preprint arXiv:1912.04187},
year = {2023}
}
备注
63 pages; v3: perturbative version of the Viterbo conjecture now proven for arbitrary symplectic capacities, added more properties to the normal form, added a statement on the local rigidity of Zoll contact forms