An oriented equator of ${𝕊}^2$ is the image of an oriented embedding ${𝕊}^1\hookrightarrow {𝕊}^2$ such that it divides ${𝕊}^2$ 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 ${𝜖}_{q+}$ the space of oriented equators. We define the Hofer girth of an embedding $j:{𝕊}^2\hookrightarrow {𝜖}_{q+}$ as the infimum of the Hofer diameter of $j^{\prime }({𝕊}^2)$, where $j^{\prime }$ is homotopic to $j$. There is a natural embedding $i_0:{𝕊}^2\hookrightarrow {𝜖}_{q+}$, 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 $i_0$.

有向赤道${𝕊}^2$是定向嵌入的图像${𝕊}^1\hookrightarrow {𝕊}^2$这样它就可以划分${𝕊}^2$分成面积相等的两半。遵循切卡诺夫，我们将两个有向赤道之间的霍弗距离定义为哈密顿微分同胚的最小霍弗范数。考虑${𝜖}_{q+}$定向赤道空间。我们定义嵌入的 Hofer 周长$j：{𝕊}^2\hookrightarrow {𝜖}_{q+}$作为 Hofer 直径的下确界$j^{\prime }（{𝕊}^2）$， 在哪里$j^{\prime }$是同伦于$j$。有一种自然的嵌入${我}_0：{𝕊}^2\hookrightarrow {𝜖}_{q+}$，将球体上的一点发送到与其垂直的正向大圆。在本文中，我们提供了 Hofer 周长的上限${我}_0$。