Local Lensing Geometry

  • Arlie O. Petters
  • Harold Levine
  • Joachim Wambsganss
Part of the Progress in Mathematical Physics book series (PMP, volume 21)


We showed in Chapter 8 that the critical points of a generic k-plane lensing map are either folds or cusps. The current chapter discusses in detail the qualitative features of k-plane lensing maps near fold and cusp critical points, including quantitative results for the single and double-plane cases. This is followed by a study of the local geometry of caustics under 1-parameter evolutions. These results bear on Problem M3, which includes a characterization of the local properties of critical curves and caustics in gravitational lensing.


Point Mass Positive Parity Negative Parity Critical Curve Local Convexity 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Arlie O. Petters
    • 1
  • Harold Levine
    • 2
  • Joachim Wambsganss
    • 3
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA
  3. 3.Astrophysikalisches Institut PotsdamUniversität PotsdamPotsdamGermany

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