Optical Design of Single Reflector Systems and the Monge–Kantorovich Mass Transfer Problem

By Tilmann Glimm, Vladimir Oliker. 2003

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5b1ca70276c2853cb08b5b4cbd41bf4060fae41e

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Optimal transportation, topology and uniqueness (2010, background): “Adding further restrictions beyond this twist hypothesis allowed Ma, Trudinger, Wang [72,100], and later Loeper [68], to develop a regularity theory for the map f1 : X −→ Y , embracing Delanoë [36], Caffarelli [20,21] and Urbas’ [102] results for the quadratic cost, Gangbo and McCann’s for its restr”
Regularity of Optimal Maps on the Sphere: the Quadratic Cost and the Reflector Antenna (2013, background): “Existence, regularity and uniqueness of weak and strong solutions have been addressed by several authors, among them Wang [26], Guan and Wang [14], Glimm and Oliker [13], and Oliker [20].”
Embedding Sn into Rn+1 with given integral Gauss curvature and optimal mass transport on Sn (2007, methodology): “In a simpler situation this approach was used in [29], and in [13], [14], [12] it was applied to study problems in geometrical optics.”
Application of the Wasserstein metric to seismic signals (2013, methodology): “This information is useful for problems in image registration [13], meteorology [7], mesh generation [6], reflector design [12], and astrophysics [8].”
Continuity, curvature, and the general covariance of optimal transportation (2007, background): “The restriction of the cost function c(x, x̄) = − log |x − x̄| from R × R to the unit sphere M = M̄ = Sn−1 := ∂Bn1(0) arises in conjunction [53], [24] with the reflector antenna problem studied by Caffarelli, Glimm, Guan, Gutierrez, Huang, Kochengin, Marder, Newman, Oliker, Waltmann, Wang, and Wesco”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, background): “Prior to that there were regularity results only for a few special costs, such as: Example 4.1 (Bilinear cost). c(x, y) = −x · y or equivalently c(x, y) = |x− y|2/2 [38] [18] [19] [135], and its restriction to M± = ∂B1(0) in R n (Gangbo and McCann [60]); Example 4.2 (Logarithmic cost; conformal geom”