Michael H. Albert

The measure contraction property on Grushin spaces

We determine the sharp measure contraction exponents of two families of Grushin-type metric measure spaces. The radial Grushin space $\mathbb{G}^{n+m}$ is $\mathbb{R}^{n}\times\mathbb{R}^{m}$, equipped with Lebesgue measure and generated by $X_i=\partial_{x_i}$ and $Y_j=|x|\partial_{y_j}$, for $1\leq i\leq n$ and $1\le...