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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.MG2023
Hadwiger's problem for bodies with enough sub-Gaussian marginals
Daniel Galicer, Joaquín Singer
Hadwiger's conjecture in convex geometry, formulated in 1957, states that every convex body in can be covered by translations of its interior. Despite signific…