(1)圆柱非局部最小曲面的非连通性及粘滞性

S. Dipierro, F. Onoue, E. Valdinoci
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引用次数: 4

摘要

我们考虑圆柱体上的非局部极小曲面,该曲面的给定基准面由板的补边给出。我们表明,当板的宽度较大时,最小化器是断开的,当板的宽度较小时,最小化器是连接的。这一特征与最小曲面的经典情况是一致的。然而,我们表明,当板的宽度较大时,最小值不是平盘,就像在经典设置中发生的那样,特别是在维度$2$中,我们提供了最小值所表现出的粘性特性的定量界限。此外,与经典情况不同,我们表明,当板的宽度很小时,最小化器完全粘附在圆柱体的侧面,从而提供了粘滞现象的进一步示例。
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(Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property
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.
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