Shouhei Honda

Regularity and structure of spaces with synthetic Ricci bounds and positive injectivity radius

In the paper, we develop a structure theory for metric measure spaces with synthetic lower Ricci curvature bounds, known as RCD spaces. Under a positive injectivity-radius assumption, we recover a smooth differential structure and prove a regularity result: such spaces are $W^{1,p}_{\mathrm{loc}}\cap C^{0,\alpha}_{\mat...