Determinants of Laplacians on Surfaces

  • Peter Sarnak
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 7)


In modern quantum geometry of strings and especially in the so-called Polyakov string model [P] determinants of Laplacians play a crucial role. As a result the study of this quantity and in particular its dependence on the metric, has been very productive. Our aim here is to review some recent developments in one aspect of this subject and to point out a number of unexpected relationships. Many of the results and ideas discussed here were obtained in collaboration with B. Osgood and R. Phillips and appear in the paper [O-P-S].


Constant Curvature Geodesic Curvature Conformal Class Selberg Zeta Function Bieberbach Conjecture 
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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Peter Sarnak
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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