2 papers
math.DG2008
Concentration of measure via approximated Brunn--Minkowski inequalities
Masayoshi Watanabe
We prove that an approximated version of the Brunn--Minkowski inequality with volume distortion coefficient implies a Gaussian concentration-of-measure phenomenon. Our main theorem…
math.DG2006
Local cut points and metric measure spaces with Ricci curvature bounded below
Masayoshi Watanabe
A local cut point is by definition a point that disconnectes its sufficiently small neighborhood. We show that there exists an upper bound for the degree of a local cut point in a…