The Li-Yau inequality and applications under a curvature-dimension condition
The Li-Yau inequality and applications under a curvature-dimension condition
We prove a global Li-Yau inequality for a general Markov semigroup under a curvature-dimension condition. This inequality is stronger than all classical Li-Yau type inequalities known to us. On a Riemannian manifold, it is equivalent to a new parabolic Harnack inequality, both in negative and positive curvature, giving new subsequents …