辛球的影子有多大？
辛几何
2013-11-11 v3 动力系统
摘要
考虑一个 2n 维单位球通过开辛嵌入映射到 2n 维标准辛向量空间中的像。其 2k 维影子是指该像在实维数为 2k 的复子空间上的正交投影。该 2k 维影子的体积是否至少等于单位 2k 维球的体积？当 k = n 时，该命题显然成立；而当 k = 1 时，它等价于 Gromov 非挤压定理的一种重述。因此，该问题可视为非挤压定理的中等维度推广。我们在线性、非线性及微扰设定下研究了该命题的有效性。
引用
@article{arxiv.1202.3614,
title = {How large is the shadow of a symplectic ball?},
author = {Alberto Abbondandolo and Rostislav Matveyev},
journal= {arXiv preprint arXiv:1202.3614},
year = {2013}
}
备注
Final version, identical to the published one. Added comments about the relationship with a conjecture of Viterbo and related references. Some of the results of this paper are contained in our previous preprint arXiv:1105.2931, which is no longer updated and will never become a published article