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math.MG2025
Monotonicity of the deficit in the local log-Brunn-Minkowski inequality
Shouda Wang
We establish a monotonicity property of the deficit associated with the local log-Brunn-Minkowski inequality (LLBM) under addition of line segments. As a corollary, if the LLBM hol…
math.MG2025
On Minkowski's monotonicity problem
Ramon van Handel, Shouda Wang
We address an old open question in convex geometry that dates back to the work of Minkowski: what are the equality cases of the monotonicity of mixed volumes? The problem is equiva…
math.AG2025
Realizations of homology classes and projection areas
Daoji Huang, June Huh, Mateusz Michałek +2
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this…