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math.AP2026
Monotonicity formulas in positively curved settings with applications to two-phase free boundary problems
Johannes Hosle
Inspired by the monotonicity formula of Alt, Caffarelli, and Friedman, we consider a natural variant of the ACF functional in positively curved 2-dimensional settings where we inte…
math.AP2020
On the -Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures
Johannes Hosle, Alexander V. Kolesnikov, Galyna V. Livshyts
We study several of the recent conjectures in regards to the role of symmetry in the inequalities of Brunn-Minkowski type, such as the -Brunn-Minkowski conjecture of Böröczky,…