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Letters in Mathematical Physics

, Volume 83, Issue 1, pp 13–18 | Cite as

Yamabe Solitons, Determinant of the Laplacian and the Uniformization Theorem for Riemann Surfaces

  • Luca Fabrizio Di Cerbo
  • Marcelo Mendes Disconzi
Article

Abstract

In this letter, we prove that non-trivial compact Yamabe solitons or breathers do not exist. In particular our proof in the two dimensional case depends only on properties of the determimant of the Laplacian and turns out to be independent of the classical uniformization theorem (UT). Using this remarkable fact we are able to explain how an independent proof of the UT for Riemann surfaces can be obtained using the Yamabe–Ricci flow.

Keywords

Yamabe flow Yamabe solitons determinant of Laplacian 

Mathematics Subject Classification (2000)

53C44 58J52 

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Copyright information

© Springer 2007

Authors and Affiliations

  • Luca Fabrizio Di Cerbo
    • 1
  • Marcelo Mendes Disconzi
    • 1
  1. 1.Department of MathematicsStony Brook UniversityStony BrookUSA

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