| Abstract: |
| In 1976, Brascamp and Lieb showed that the log-concavity of the initial datum is preserved by the heat flow in a convex domain of Euclidean space, and this has always been considered an optimal property.
In a joint work with Kazuhiro Ishige and Paolo Salani, we doubted the optimality of the log-concavity. We introduced power-logconcavities a refinement of the log-concavity and claryfied the strongest concavity property among all admisslble concavities preserved by the heat flow in a convex domain of Euclidean space. I will present some related inequalities. |
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