Only ellipsoids have caustics
type: Item
instance of: scholarly article
title: Only ellipsoids have caustics
zbMATH Open document ID: 0847.34052
DOI: 10.1007/BF01460986
author: Peter M. Gruber
published in: Mathematische Annalen
publication date: 1996-10-08T00:00:00Z
full work available at URL: https://eudml.org/doc/165364
review text: The author studies the existence problem for the caustics of billiard tables in Euclidean \(d\)-space \(E^d\) for \(d\geq 3\). His main result is that among all convex billiard tables in \(E^d\), \(d\geq 3\), only the solid ellipsoids have convex caustics; The caustics are precisely the confocal solid ellipsoids contained in their interiors and, moreover, the intersection of these. This result settles one conjecture in the author's own paper [Geom. Dedicata 33, 205-226 (1990; Zbl 0696.52001)].
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 840181
zbMATH Keywords: caustics of billiard tables
zbMATH Keywords: ellipsoids
zbMATH Keywords: convex caustics
reviewed by: Duo Wang
MaRDI profile type: Publication
cites work: Q4167627
cites work: Q3198453
cites work: Seules les quadriques admettent des caustiques
cites work: On the second differentiability of convex surfaces
cites work: Characterizations of ellipsoids
cites work: Unsolved problems in geometry
cites work: Convex billiards
cites work: Q5509729
cites work: Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki
cites work: Q4002287
cites work: Q3997178
cites work: Q5640131
cites work: Q5671313
cites work: Q3314627
cites work: Q3294369
cites work: Q4004053
cites work: Q5287551
description: scientific article; zbMATH DE number 840181