A characterization of the rate of change of $\Phi$-entropy via an integral form curvature-dimension condition

Dejun Luo

Let $M$ be a compact Riemannian manifold without boundary and $V:M\to \mathbb{R}$ a smooth function. Denote by $P_t$ and $\mathrm{d}\mu =e^V\mathrm{d}x$ the semigroup and symmetric measur…