Bourgain’s slicing problem and KLS isoperimetry up to polylog

By Bo'az Klartag, Joseph Lehec. Geometric and Functional Analysis, 2022

88 citations recorded by the source corpus.

We prove that Bourgain’s hyperplane conjecture and the Kannan-Lovász-Simonovits (KLS) isoperimetric conjecture hold true up to a factor that is polylogarithmic in the dimension.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/93da7e7675c70a5b7e7acdda95b794bca08b9faf

How researchers see this paper

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In Applied Mathematics

1. Bo'az Klartag
2. Grigoris Paouris
3. Emanuel Milman
4. Joseph Lehec
5. Radosław Adamczak
6. Matthieu Fradelizi
7. Elisabeth M. Werner
8. Mathieu Meyer

In Discrete Mathematics and Combinatorics

1. Bo'az Klartag

In Geometry and Topology

1. Bo'az Klartag
2. Filippo Santambrogio
3. Grigoris Paouris

Citations in the corpus

• Logarithmic bounds for isoperimetry and slices of convex sets (2023, background): “Two years ago, a breakthrough by Chen [14] led to the bound Ln ≤ exp ( C √ log n · log logn ) which was subsequently improved to Ln ≤ C log(4) n by Klartag and Lehec [33], to Ln ≤ C log n by Jambulapati, Lee and Vempala [24] and to Ln ≤ C log by Lehec (personal communication).”