On the geometry of convex reflectors

• Autorzy: Vladimir I. Oliker
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C45: Global surface theory (convex surfaces \`a la A. D. Aleksandrov)
• 78A05: Geometric optics
• 52A20: Convex sets in n dimensions (including convex hypersurfaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2002
• Tom: 57
• Numer: 1
• Strony: 155-169

Daty

wydano

2002

Twórcy

autor

Vladimir I. Oliker

• Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, U.S.A.

Identyfikatory

DOI

10.4064/bc57-0-10