A Minkowski-style theorem for focal functions of compact convex reflectors
| dc.creator | Oliker, Vladimir | |
| dc.date | 2006-12-26 | |
| dc.date.accessioned | 2026-07-07T07:37:08Z | |
| dc.date.available | 2026-07-07T07:37:08Z | |
| dc.description | This paper continues the study of a class of compact convex hypersurfaces in Euclidean space $R^{n+1}, ~n \geq 1$, which are boundaries of compact convex bodies obtained by taking the intersection of (solid) confocal paraboloids of revolution. Such hypersurfaces are called reflectors. In $R^3$ reflectors arise naturally in geometrical optics and are used in design of light reflectors and reflector antennas. They are also important in rendering problems in computer graphics. The notion of a focal function for reflectors plays a central role similar to that of the Minkowski support function for convex bodies. In this paper the basic question of when a given function is a focal function of a convex reflector is answered by establishing necessary and sufficient conditions. In addition, some smoothness properties of reflectors and of the associated directrix hypersurfaces are also etablished. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0612757 | |
| dc.identifier | http://arxiv.org/abs/math/0612757 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120669 | |
| dc.subject | Differential Geometry | |
| dc.subject | 52A20, 35J65, 78A05 | |
| dc.title | A Minkowski-style theorem for focal functions of compact convex reflectors | |
| dc.type | text |