Abstract
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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Dujardin, R., Guedj, V. (2011). Geometric Properties of Maximal psh Functions. In: Guedj, V. (eds) Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Lecture Notes in Mathematics(), vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23669-3_3
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DOI: https://doi.org/10.1007/978-3-642-23669-3_3
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23668-6
Online ISBN: 978-3-642-23669-3
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