Affirmative Resolution of Bourgain's Slicing Problem using Guan's Bound
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916534029385728 |
|---|---|
| author | Klartag, Boaz Lehec, Joseph |
| author_facet | Klartag, Boaz Lehec, Joseph |
| contents | We provide the final step in the resolution of Bourgain's slicing problem in the affirmative. Thus we establish the following theorem: for any convex body $K \subseteq \mathbb{R}^n$ of volume one, there exists a hyperplane $H \subseteq \mathbb{R}^n$ such that $$ Vol_{n-1}(K \cap H) > c, $$ where $c > 0$ is a universal constant. Our proof combines Milman's theory of $M$-ellipsoids, stochastic localization with a recent bound by Guan, and stability estimates for the Shannon-Stam inequality by Eldan and Mikulincer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affirmative Resolution of Bourgain's Slicing Problem using Guan's Bound Klartag, Boaz Lehec, Joseph Metric Geometry Functional Analysis Probability We provide the final step in the resolution of Bourgain's slicing problem in the affirmative. Thus we establish the following theorem: for any convex body $K \subseteq \mathbb{R}^n$ of volume one, there exists a hyperplane $H \subseteq \mathbb{R}^n$ such that $$ Vol_{n-1}(K \cap H) > c, $$ where $c > 0$ is a universal constant. Our proof combines Milman's theory of $M$-ellipsoids, stochastic localization with a recent bound by Guan, and stability estimates for the Shannon-Stam inequality by Eldan and Mikulincer. |
| title | Affirmative Resolution of Bourgain's Slicing Problem using Guan's Bound |
| topic | Metric Geometry Functional Analysis Probability |
| url | https://arxiv.org/abs/2412.15044 |