LEADER 02755nam 22004215a 450 001 9910157636803321 005 20161219234501.0 010 $a3-03719-667-X 024 70$a10.4171/167 035 $a(CKB)3710000001001505 035 $a(CH-001817-3)210-161219 035 $a(PPN)197870120 035 $a(EXLCZ)993710000001001505 100 $a20161219j20170112 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$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 LEADER 01371nam a2200361 i 4500 001 991000904349707536 005 20020507175553.0 008 940228s1986 us ||| | eng 020 $a0691084130 035 $ab10773629-39ule_inst 035 $aLE01304096$9ExL 040 $aDip.to Matematica$beng 082 0 $a515.353 084 $aAMS 35A 084 $aAMS 35A27 084 $aQA300.K3713 100 1 $aKashiwara, Masaki$047448 245 10$aFoundations of algebraic analysis /$cMasaki Kashiwara, Takahiro Kawai, Tatsuo Kimura ; transl. Goro Kato 260 $aPrinceton :$bPrinceton Univ. Press,$c1986 300 $axii, 254 p. ;$c24 cm 490 0 $aPrinceton mathematical series,$x0079-5194 ;$v37 500 $aTransl. from Japanese 650 0$aMicrolocal methods 650 0$aPartial differential equations 700 1 $aKawai, Takahiro$eauthor$4http://id.loc.gov/vocabulary/relators/aut$047449 700 1 $aKimura, Tatsuo$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0442072 700 1 $aKato, Goro 907 $a.b10773629$b23-02-17$c28-06-02 912 $a991000904349707536 945 $aLE013 35A KAS11 (1986)$g1$i2013000002996$lle013$o-$pE0.00$q-$rl$s- $t0$u0$v0$w0$x0$y.i10872280$z28-06-02 996 $aFoundations of algebraic analysis$982407 997 $aUNISALENTO 998 $ale013$b01-01-94$cm$da $e-$feng$gus $h0$i1