• Wei Zeng
  • Xianfeng David Gu
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


This chapter briefly introduces the fundamental concepts of shape space and mapping space, including different transformation groups (such as diffeomorphisms, isometries, conformal transformations, and rigid motions) and group actions on shape spaces. In order to perform surface registration and shape analysis in the shape space and the mapping space, Ricci flow is introduced, which leads to the celebrated uniformization theorem.


Harmonic Mapping Riemann Surface Quotient Space Homotopy Class Conformal Module 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Wei Zeng
    • 1
  • Xianfeng David Gu
    • 2
  1. 1.Computing and Information ScienceFlorida International UniversityMiamiUSA
  2. 2.Computer ScienceState University of New YorkStony BrookUSA

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