Strict concavity properties of cross covariograms
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908479724191744 |
|---|---|
| author | Bianchi, Gabriele Burchard, Almut Lin, Lawrence |
| author_facet | Bianchi, Gabriele Burchard, Almut Lin, Lawrence |
| contents | It is well-known that the cross covariogram of two convex bodies in n dimensions is 1/n-concave on its support. This paper provides conditions for strict 1/n-concavity in dimension n>1, and an analysis of how it can fail. Among the implications are that (i.) the cross covariogram of strictly convex bodies is strictly 1/n-concave, unless one body contains a translate of the other in its interior, and (ii.) the cross covariogram of an arbitrary convex body with its reflection through the origin is strictly log-concave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strict concavity properties of cross covariograms Bianchi, Gabriele Burchard, Almut Lin, Lawrence Metric Geometry Functional Analysis 52A38 (primary) 26D15, 60D05 (secondary) It is well-known that the cross covariogram of two convex bodies in n dimensions is 1/n-concave on its support. This paper provides conditions for strict 1/n-concavity in dimension n>1, and an analysis of how it can fail. Among the implications are that (i.) the cross covariogram of strictly convex bodies is strictly 1/n-concave, unless one body contains a translate of the other in its interior, and (ii.) the cross covariogram of an arbitrary convex body with its reflection through the origin is strictly log-concave. |
| title | Strict concavity properties of cross covariograms |
| topic | Metric Geometry Functional Analysis 52A38 (primary) 26D15, 60D05 (secondary) |
| url | https://arxiv.org/abs/2508.03887 |