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math.FA2025
Some comments on the mth-order Projection Bodies
Dylan Langharst
The celebrated Petty's projection inequality is a sharp upper bound for the volume of the polar projection body of a convex body. Lutwak introduced the concept of mixed projection…
math.FA2025
On Moment-Entropy inequalities in the space of matrices
Dylan Langharst
In a series of works, Lutwak, Yang and Zhang established what could be called affine information theory, which is the study of moment-entropy and Fisher-information-type inequaliti…
math.FA2021★ 12 cited
Weighted Minkowski's Existence Theorem and Projection Bodies
Liudmyla Kryvonos, Dylan Langharst
The Brunn-Minkowski Theory has seen several generalizations over the past century. Many of the core ideas have been generalized to measures. With the goal of framing these generali…