Measure theoretic Rogers-Shephard and Zhang type inequalities

Analysis Seminar
Wednesday, February 9, 2022 - 2:00pm for 1 hour (actually 50 minutes)
ONLINE (Zoom link in abstract)
Michael Roysdon – Tel Aviv University –
Benjamin Jaye

This talk will detail two recent papers concerning Rogers-Shephard inequalities and Zhang inequalities for various classes of measures, the first of which is a reverse form of the Brunn-Minkowsk inequality, and the second of which can be seen to be a reverse affine isoperimetric inequality; the feature of both inequalities is that they each provide a classification of the n-dimensional simplex in the volume case. The covariogram of a measure plays an essential role in the proofs of each of these inequalities. In particular, we will discuss a variational formula concerning the covariogram resulting in a measure theoretic version of the projection body, an object which has recently gained a lot of attention--these objects were previously studied by Livshyts in her analysis of the Shephard problem for general measure.


The talk will be on Zoom via the link