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101 0 $aeng
135   $aurnn|mmmmamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aDegenerate Complex Monge-Ampe?re Equations$b[electronic resource] /$fVincent Guedj, Ahmed Zeriahi
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2017
215   $a1 online resource (496 pages)
225 0 $aEMS Tracts in Mathematics (ETM)$v26
311   $a3-03719-167-8 
330   $aWinner of the 2016 EMS Monograph Award!  Complex Monge-Ampe?re equations have been one of the most powerful tools in Ka?hler geometry since Aubin and Yau's classical works, culminating in Yau's solution to the Calabi conjecture. A notable application is the construction of Ka?hler-Einstein metrics on some compact Ka?hler manifolds. In recent years degenerate complex Monge-Ampe?re equations have been intensively studied, requiring more advanced tools.  The main goal of this book is to give a self-contained presentation of the recent developments of pluripotential theory on compact Ka?hler manifolds and its application to Ka?hler-Einstein metrics on mildly singular varieties. After reviewing basic properties of plurisubharmonic functions, Bedford-Taylor's local theory of complex Monge-Ampe?re measures is developed. In order to solve degenerate complex Monge-Ampe?re equations on compact Ka?hler manifolds, fine properties of quasi-plurisubharmonic functions are explored, classes of finite energies defined and various maximum principles established. After proving Yau's celebrated theorem as well as its recent generalizations, the results are then used to solve the (singular) Calabi conjecture and to construct (singular) Ka?hler-Einstein metrics on some varieties with mild singularities.  The book is accessible to advanced students and researchers of complex analysis and differential geometry.
606   $aComplex analysis$2bicssc
606   $aSeveral complex variables and analytic spaces$2msc
615 07$aComplex analysis
615 07$aSeveral complex variables and analytic spaces
676   $a515.9
686   $a32-xx$2msc
700   $aGuedj$b Vincent$0524796
702   $aZeriahi$b Ahmed
801  0$bch0018173
906   $aBOOK
912   $a9910157636803321
996   $aDegenerate Complex Monge-Ampe?re Equations$92564449
997   $aUNINA