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math.MG2025
Extensions of the Busemann-Petty Problem for Arbitrary Measures
Daniel Galicer, Julián Haddad, Joaquín Singer
The classical Busemann--Petty problem asks whether smaller central hyperplane sections of origin-symmetric convex bodies imply smaller total volume. Zvavitch studied the analogous…
math.MG2025
On the polar of Schneider's difference body
Julián Haddad, Dylan Langharst, Galyna V. Livshyts +1
In 1970, Schneider introduced the th-order extension of the difference body of a convex body , the convex body in . He conject…