论文标题
球体上的分数周围
Fractional perimeters on the sphere
论文作者
论文摘要
本说明可以治疗球体分数周围或球上$ s $ perimeter的几个问题。建立了球形分数等级不平等。事实证明，平等案例正是球形盖。此外，事实证明，分数周围与表面积的融合已证明是$ s \ searlrow 1 $。结果表明，他们的限制为$ s \ searrow -\ infty $可以用卷来表示。
This note treats several problems for the fractional perimeter or $s$-perimeter on the sphere. The spherical fractional isoperimetric inequality is established. It turns out that the equality cases are exactly the spherical caps. Furthermore, the convergence of fractional perimeters to the surface area as $s \nearrow 1$ is proven. It is shown that their limit as $s \searrow -\infty$ can be expressed in terms of the volume.
