论文标题
在凸面或凹室域的拉格朗日能力上
On the Lagrangian capacity of convex or concave toric domains
论文作者
论文摘要
我们建立了有关拉格朗日容量的计算结果，最初由Cieliebak-Mohnke定义。更确切地说，我们表明，4维凸圆形域的拉格朗日能力等于其对角线。在假设有一个合适的虚拟扰动方案的假设下工作，该方案定义了线性化接触同源性的曲线计数，我们将先前的结果扩展到任何凸或凹形旋转圆形域。该结果对Cieliebak-Mohnke的猜想为椭圆形能力提供了积极的答案。
We establish computational results concerning the Lagrangian capacity, originally defined by Cieliebak-Mohnke. More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric domain is equal to its diagonal. Working under the assumption that there is a suitable virtual perturbation scheme which defines the curve counts of linearized contact homology, we extend the previous result to any convex or concave toric domain. This result gives a positive answer to a conjecture of Cieliebak-Mohnke for the Lagrangian capacity of the ellipsoid.
