Distances between non--symmetric convex bodies and the $MM^*$-estimate
| dc.creator | Rudelson, M. | |
| dc.date | 1998-12-01 | |
| dc.date.accessioned | 2026-07-07T05:27:04Z | |
| dc.date.available | 2026-07-07T05:27:04Z | |
| dc.description | Let $K, D$ be $n$-dimensional convex bodes. Define the distance between $K$ and $D$ as $$ d(K,D) = \inf \{λ| T K \subset D+x \subset λ\cdot TK \}, $$ where the infimum is taken over all $x \in R^n$ and all invertible linear operators $T$. Assume that 0 is an interior point of $K$ and define $$ M(K) =\int_{S^{n-1}} \| ω\|_K d μ(ω), $$ where $μ$ is the uniform measure on the sphere. Let $K^{\circ}$ be the polar body of $K$. We use the difference body estimate to prove that $K$ can be embedded into $R^n$ so that $$ M(K) \cdot M(K^{\circ}) \le C n^{1/3} \log^a n $$ for some absolute constants $C$ and $a$. We apply this result to show that the distance between two $n$-dimensional convex bodies does not exceed $n^{4/3}$ up to a logarithmic factor. | |
| dc.description | 15 pages, AMSTeX | |
| dc.identifier | https://arxiv.org/abs/math/9812010 | |
| dc.identifier | http://arxiv.org/abs/math/9812010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77789 | |
| dc.subject | Functional Analysis | |
| dc.subject | Metric Geometry | |
| dc.subject | 46B07, 46B09 52A20 | |
| dc.title | Distances between non--symmetric convex bodies and the $MM^*$-estimate | |
| dc.type | text |