63 citations · 66 across the 7 of their papers we have counts for
7 papers
Designing double freeform surfaces for collimated beam shaping with optimal mass transportation and linear assignment problems
Leonid L. Doskolovich, Dmitry A. Bykov, Evgeniy S. Andreev +2
We propose a method for designing refractive optical elements for collimated beam shaping. In this method, the problem of finding a ray mapping is formulated as a linear assignment…
A characterization of revolution quadrics by a system of partial differential equations
Vladimir Oliker
It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topo…
Kummer configurations and reflector problems: Hypersurfaces in $\Rn$ with given mean intensity
Vladimir Oliker
For a congruence of straight lines defined by a hypersurface in and a field of reflected directions created by a point source we define the notion of intensity…
Uniqueness of starshaped compact hypersurfaces with prescribed -th mean curvature in hyperbolic space
J. Lucas M. Barbosa, Jorge H. S. de Lira, Vladimir Oliker
Let be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurface for which , when evaluated on , coinci…
Existence of optimal maps in the reflector-type problems
Wilfrid Gangbo, Vladimir Oliker
In this paper, we consider probability measures and on a --dimensional sphere in $\Rd, d \geq 1,$ and cost functions of the form $c(\x,\y)=l(\frac{|\x-\y|^2}{2})$ that g…
A Minkowski-style theorem for focal functions of compact convex reflectors
Vladimir Oliker
This paper continues the study of a class of compact convex hypersurfaces in Euclidean space , which are boundaries of compact convex bodies obtained by taking…