Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below

We study decreasing rearrangements of functions defined on (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by and dimension bounded above by in a synthetic sense, the so called spaces. We first establish a Polya-Szego type inequality stating that the -Sobolev norm d...