The slicing problem by bourgain

B. Klartag*, V. Milman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In the context of his work on maximal functions in the 1980s, Jean Bourgain came across the following geometric question: Is there c > 0 such that for any dimension n and any convex body K ⊆ Rn of volume one, there exists a hyperplane H such that the (n-1)-dimensional volume of K ∩ H is at least c? This innocent and seemingly obvious question (which remains unanswered!) has established a new direction in high-dimensional geometry. It has emerged as an "engine" that inspired the discovery of many deep results and unexpected connections. Here we provide a survey of these developments, including many of Bourgain's results.

Original languageEnglish
Title of host publicationAnalysis at Large
Subtitle of host publicationDedicated to the Life and Work of Jean Bourgain
PublisherSpringer International Publishing
Number of pages29
ISBN (Electronic)9783031053313
ISBN (Print)9783031053306
StatePublished - 1 Nov 2022


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