A survey of mass partitions
E Roldán-Pensado, P Soberón - Bulletin of the American Mathematical …, 2022 - ams.org
Mass partition problems describe the partitions we can induce on a family of measures or
finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this …
finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this …
Using the KKM theorem
D McGinnis, S Zerbib - arXiv preprint arXiv:2408.03921, 2024 - arxiv.org
The KKM theorem, due to Knaster, Kuratowski, and Mazurkiewicz in 1929, is a fundamental
result in fixed-point theory, which has seen numerous extensions and applications. In this …
result in fixed-point theory, which has seen numerous extensions and applications. In this …
A problem related to Bárány–Grünbaum conjecture
PVM Blagojević, AD Blagojević - Filomat, 2013 - JSTOR
In this paper we prove that for any absolute continuous Borel probability measure 𝜇 on the
sphere 𝑆² and any t∈[0, 1 4] there exist four great semi-circles 𝓁₁,..., 𝓁₄ emanating from a …
sphere 𝑆² and any t∈[0, 1 4] there exist four great semi-circles 𝓁₁,..., 𝓁₄ emanating from a …