On the geometry of convex reflectors

Vladimir I. Oliker. "On the geometry of convex reflectors." Banach Center Publications 57.1 (2002): 155-169. <http://eudml.org/doc/282125>.

@article{VladimirI2002,
abstract = {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.},
author = {Vladimir I. Oliker},
journal = {Banach Center Publications},
keywords = {convex surface; focal function; Minkowski problem},
language = {eng},
number = {1},
pages = {155-169},
title = {On the geometry of convex reflectors},
url = {http://eudml.org/doc/282125},
volume = {57},
year = {2002},
}

TY - JOUR
AU - Vladimir I. Oliker
TI - On the geometry of convex reflectors
JO - Banach Center Publications
PY - 2002
VL - 57
IS - 1
SP - 155
EP - 169
AB - 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.
LA - eng
KW - convex surface; focal function; Minkowski problem
UR - http://eudml.org/doc/282125
ER -