New characterizations of log-concavity via Dirichlet heat flow

We study the strongest concavity property preserved by the Dirichlet heat flow, characterizing log-concavity in this connection. To this aim, we also review and investigate the notion of F-concavity, which largely generalizes the usual concavity. As side results, by the use of the notions of closedness under positive scalar multiplication and closedness under positive exponentiation, we characterize power concavity and power log-concavity among nontrivial F-concavities, respectively (showing in particular that log-concavity is the only F-concavity which is closed both under positive scalar multiplication and positive exponentiation).