论文标题
局部刚性，接触同构和保形因子
Local rigidity, contact homeomorphisms, and conformal factors
论文作者
论文摘要
我们表明，如果在触点同构中的传奇人物submanifold的图像（即，同构为$ c^0 $ - 接触型的限制的同态性）是平稳的，那么它是legendrian，它只是在近似近似接触术的共同因素上仅积极的局部降低界限。在Arxiv的意义上，更一般而言的类似结果是共截相的亚策略：1306.6367。这是humilière-leclercq-seyfaddini坐骨的固定刚性定理，$ c^0 $ symbletectic几何形状，证明是基于局部封闭子集的当地点的局部刚性的刻度，改编了作者的最新重新定义：1912.13043。我们还提供了两种不同的示例口味，表明触点同构可以映射一个横向接触结构的子手：在某个点上与接触结构平滑且切线的子手机。
We show that if the image of a Legendrian submanifold under a contact homeomorphism (i.e. a homeomorphism that is a $C^0$-limit of contactomorphisms) is smooth then it is Legendrian, assuming only positive local lower bounds on the conformal factors of the approximating contactomorphisms. More generally the analogous result holds for coisotropic submanifolds in the sense of arXiv:1306.6367. This is a contact version of the Humilière-Leclercq-Seyfaddini coisotropic rigidity theorem in $C^0$ symplectic geometry, and the proof adapts the author's recent re-proof of that result in arXiv:1912.13043 based on a notion of local rigidity of points on locally closed subsets. We also provide two different flavors of examples showing that a contact homeomorphism can map a submanifold that is transverse to the contact structure to one that is smooth and tangent to the contact structure at a point.
