论文标题
（dis）圆柱体中非局部最小表面的连接性和粘性特性
(Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property
论文作者
论文摘要
我们考虑在圆柱体中的非局部最小表面，并具有由平板的补充给出的规定基准。我们表明，当平板的宽度很大时，最小化器会断开连接，而当平板的宽度很小时，最小化器就会连接。此功能与最小表面的经典情况一致。 然而，我们表明，当平板的宽度很大时，最小化器不是平坦的圆盘，因为它在经典环境中发生，尤其是在尺寸$ 2 $中，我们为最小化器所展示的粘性属性提供了定量界限。 此外，与经典案例不同，我们表明，当平板的宽度很小时，最小化器就会完全粘附在圆柱体的侧面，从而提供了粘性现象的进一步例子。
We consider nonlocal minimal surfaces in a cylinder with prescribed datum given by the complement of a slab. We show that when the width of the slab is large the minimizers are disconnected and when the width of the slab is small the minimizers are connected. This feature is in agreement with the classical case of the minimal surfaces. Nevertheless, we show that when the width of the slab is large the minimizers are not flat discs, as it happens in the classical setting, and, in particular, in dimension $2$ we provide a quantitative bound on the stickiness property exhibited by the minimizers. Moreover, differently from the classical case, we show that when the width of the slab is small then the minimizers completely adhere to the side of the cylinder, thus providing a further example of stickiness phenomenon.
