Euclidean forward-reverse Brascamp-Lieb inequalities: finiteness, structure, and extremals (Q2024673)

The main object of the investigations are Euclidean forward-reverse Brascamp-Lieb inequalities. These inequalities imply many other classical inequalities in analysis and geometry, such as the Hölder inequality, the Young inequality, and the Loomis-Whitney inequality. It is proved that the centered Gaussian functions saturate the Euclidean forward-reverse Brascamp-Lieb inequalities. It extends the Brascamp-Lieb and Barthe theorems. The fact that the best constants in the Brascamp-Lieb and Barthe inequalities are equal is generalized by developing a duality principle for best constants.