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 $(X,d,\mu )$ supporting a $(1,1)$-Poincaré inequality, we show that for all $0<\theta <1$, the following fractional Poincaré ineq…