Florentin Münch (Potsdam)
We introduce a new version of curvature dimension inequality. We use this to prove a logarithmic Li-Yau inequality on graphs. To formulate this inequality, we use a non-linear ariant of the calculus of Bakry and Emery. In the case of manifolds, the new calculus and the new curvature dimension inequality coincide with the common ones. In the case of graphs, they coincide in a limit. In this sense, the new curvature-dimension inequality gives a more general concept of curvature on graphs and on manifolds. Moreover, a variety of non-logarithmic Li-Yau type gradient estimates can be obtained by using the new Bakry-Emery type calculus.