Infinite geodesic rays in the space of Kähler potentials

• Claudio Arezzo ^[2] ; Gang Tian ^[1]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
  2. [2] Università di Parma, Italy
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 2, Nº 4, 2003, págs. 617-630
• Idioma: inglés
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• Resumen

  • In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults to the existence problem for extremal metrics.