论文标题
圆环域的符号非跨性别
Symplectic non-convexity of toric domains
论文作者
论文摘要
我们研究了$ \ mathbb r^4 $中星形圆形域的符号切除型（称为Symbletectic suvexity）的凸度。特别是，基于Chaidez-Edtmair的标准，通过ruelle不变性和星形圆磨域边界的收缩比，我们在域上提供基本操作，这些域可以杀死符号凸度。这些操作仅导致$ c^0 $ -small扰动在域的音量上。此外，其中一种操作是一种系统的方法，用于产生动态凸的示例，而不是符合直接凸出的圆环域。最后，我们能够为Chaidez-Edtmair标准中出现的常数提供具体的界限。
We investigate the convexity up to symplectomorphism (called symplectic convexity) of star-shaped toric domains in $\mathbb R^4$. In particular, based on the criterion from Chaidez-Edtmair via Ruelle invariant and systolic ratio of the boundary of star-shaped toric domains, we provide elementary operations on domains that can kill the symplectic convexity. These operations only result in $C^0$-small perturbations in terms of domains' volume. Moreover, one of the operations is a systematic way to produce examples of dynamically convex but not symplectically convex toric domains. Finally, we are able to provide concrete bounds for the constants that appear in Chaidez-Edtmair's criterion.
