To logconcavity and beyond

Abstract

In 1976 Brascamp and Lieb proved that the heat flow preserves logconcavity. In this paper, introducing a variation of concavity, we show that it preserves in fact a stronger property than logconcavity and we identify the strongest concavity preserved by the heat flow.

We removed one result, Theorem 3.2 of the old version, due to a gap in the proof