Geometric Properties of Maximal psh Functions

  • Romain Dujardin
  • Vincent Guedj
Part of the Lecture Notes in Mathematics book series (LNM, volume 2038)


We review the geometric properties of maximal plurisubharmonic 5 functions u and of the associated closed positive currents dd c u, in two complex 6 dimensions.When u is regular enough (at least of class C3), dd c u is “foliated” 7 by Riemann surfaces along which u is harmonic. On the other hand when u is 8 less than C 1 ,1 this picture breaks down completely, as recent examples show.


Plurisubharmonic Function Ahler Form Holomorphic Disk Continuous Potential Complex Curf 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Ecole Polytechnique, CMLSPalaiseau CedexFrance
  2. 2.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouseFrance

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