Geometric inequalities related to fractional perimeter: fractional Poincaré, isoperimetric, and boxing inequalities in metric measure spaces

Josh Kline, Panu Lahti, Jiang Li +1

In the setting of a complete, doubling metric measure space $(X,d,\hat{I}¼)$ supporting a $(1,1)$-Poincaré inequality, we show that for all $0<\hat{I}¸<1$, the following fractional Poincaré…