In this paper we consider a special class of convex hypersurfaces in Euclidean space which arise as weak solutions to some inverse problems of recovering reflectors from scattering data. For this class of hypersurfaces we study the notion of the focal function which, while sharing the important convexity property with the classical support function, has the advantage of being exactly the "right tool" for such inverse problems. We also discuss briefly the close analogy between one such inverse problem and the classical Minkowski problem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-10,
author = {Vladimir I. Oliker},
title = {On the geometry of convex reflectors},
journal = {Banach Center Publications},
volume = {58},
year = {2002},
pages = {155-169},
zbl = {1020.52005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-10}
}
Vladimir I. Oliker. On the geometry of convex reflectors. Banach Center Publications, Tome 58 (2002) pp. 155-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc57-0-10/