论文标题
在大圈子领域的围栏上
On the Hofer Girth of the Sphere of Great Circles
论文作者
论文摘要
$ \ mathbb {s}^2 $的定向赤道是定向嵌入$ \ mathbb {s}^1 \ hookrightArrow \ mathbb {s}^2 $的图像。在Chekanov之后，我们将两个方向赤道之间的Hofer距离定义为Hamiltonian差异性的虚拟Hofer Norm，将一个差异置于一个彼此之间。考虑$ \ MATHCAL {E} Q _+$定向赤道的空间。我们将嵌入$ j的hofer围绕$ j：\ mathbb {s}^2 \ hookrightArrow \ mathcal {e} q _+$定义为$ j'（\ mathbb {s}^2）$ j'$ j'$ j'$ j as j as Polotopic to $ j $ j $ j $ j $ j $ j $ j $ j $ J'（\ mathbb {s}^2）的hofer直径的最低。有一个自然嵌入$ i_0：\ mathbb {s}^2 \ hookrightArrow \ mathcal {e} q _+$，在球体上向垂直于它的正向取向的大圆圈发送一个点。在本文中，我们提供了$ I_0 $的Hofer Girth上的上限。
An oriented equator of $\mathbb{S}^2$ is the image of an oriented embedding $\mathbb{S}^1 \hookrightarrow \mathbb{S}^2$ such that it divides $\mathbb{S}^2$ into two equal area halves. Following Chekanov, we define the Hofer distance between two oriented equators as the infimal Hofer norm of a Hamiltonian diffeomorphism taking one to another. Consider $\mathcal{E}q_+$ the space of oriented equators. We define the Hofer girth of an embedding $j:\mathbb{S}^2 \hookrightarrow \mathcal{E}q_+$ as the infimum of the Hofer diameter of $j'(\mathbb{S}^2)$, where $j'$ is homotopic to $j$. There is a natural embedding $i_0:\mathbb{S}^2\hookrightarrow\mathcal{E}q_+$, sending a point on the sphere to the positively oriented great circle perpendicular to it. In this paper we provide an upper bound on the Hofer girth of $i_0$.
