Mass partitions

Four hyperplanes do not always equipartition a mass in ℝ⁴

Pablo Soberón

A smooth positive density in four dimensions that admits no equipartition into sixteen equal parts by four affine hyperplanes.

Partitions of mass assignments with spheres and wedges

Deron Lessure, Pablo Soberón

Accepted in European Journal of Combinatorics

Cookie cutters: Bisections with fixed shapes

Patrick Schnider, Pablo Soberón

Adv. in Appl. Math. 171, Paper No. 102957, 15 pp.

Generalizations of the Yao–Yao partition theorem and the central transversal theorem

Michael N. Manta, Pablo Soberón

Discrete Comput. Geom. 71 (4), 1381–1402.

Bisections of mass assignments using flags of affine spaces

Ilani Axelrod-Freed, Pablo Soberón

Discrete Comput. Geom. 72 (2), 550–568.

Bisections of mass assignments by parallel hyperplanes

Nikola Sadovek, Pablo Soberón

Complex analogues of the Tverberg–Vrećica conjecture and central transversal theorems

Nikola Sadovek, Pablo Soberón

Trans. Amer. Math. Soc. 379 (2026), no. 5, 3665–3691.

Bisecting masses with families of parallel hyperplanes

Alfredo Hubard, Pablo Soberón

Lifting methods in mass partition problems

Pablo Soberón, Yuki Takahashi

Int. Math. Res. Not. IMRN 2023 (16), 14103–14130.

A survey of mass partitions

Edgardo Roldán-Pensado, Pablo Soberón

Bull. Amer. Math. Soc. 59 (2), 227–267.

Balanced convex partitions of lines in the plane

Alexander Xue, Pablo Soberón

Discrete Comput. Geom. 66 (3), 1150–1167.

Cutting a part of many measures

Pavle V. M. Blagojević, Nevena Palić, Pablo Soberón, Günter M. Ziegler

Forum of Mathematics, Sigma 7, E37.

Thieves can make sandwiches

Pavle V. M. Blagojević, Pablo Soberón

Bull. London Math. Soc. 50 (1), 108–123.

Measure Partitions Using Hyperplanes with Fixed Directions

Roman N. Karasev, Edgardo Roldán-Pensado, Pablo Soberón

Israel J. Math. 212 (2), 705–708.

An Extension of a Theorem by Yao & Yao

Edgardo Roldán-Pensado, Pablo Soberón

Discrete Comput. Geom. 51 (2), 285–289.

Balanced Convex Partitions of Measures in ℝᵈ

Pablo Soberón

Mathematika 58, 71–76.