000			02856nam a22003975a 4500
001			210-161219
003			CH-001817-3
005			20170613140840.0
006			a fot ||| 0|
007			cr nn mmmmamaa
008			161219e20170112sz fot ||| 0|eng d
020			_a9783037196670
024	7	0	_a10.4171/167 _2doi
040			_ach0018173
072		7	_aPBKD _2bicssc
084			_a32-xx _2msc
100	1		_aGuedj, Vincent, _eauthor.
245	1	0	_aDegenerate Complex Monge–Ampère Equations _h[electronic resource] / _cVincent Guedj, Ahmed Zeriahi
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2017
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2017
300			_a1 online resource (496 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Tracts in Mathematics (ETM) _v26
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_aWinner of the 2016 EMS Monograph Award! Complex Monge–Ampère equations have been one of the most powerful tools in Kähler geometry since Aubin and Yau’s classical works, culminating in Yau’s solution to the Calabi conjecture. A notable application is the construction of Kähler-Einstein metrics on some compact Kähler manifolds. In recent years degenerate complex Monge–Ampère 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 Kähler manifolds and its application to Kähler–Einstein metrics on mildly singular varieties. After reviewing basic properties of plurisubharmonic functions, Bedford–Taylor’s local theory of complex Monge–Ampère measures is developed. In order to solve degenerate complex Monge–Ampère equations on compact Kähler 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) Kähler–Einstein metrics on some varieties with mild singularities. The book is accessible to advanced students and researchers of complex analysis and differential geometry.
650	0	7	_aComplex analysis _2bicssc
650	0	7	_aSeveral complex variables and analytic spaces _2msc
700	1		_aGuedj, Vincent, _eauthor.
700	1		_aZeriahi, Ahmed, _eauthor.
856	4	0	_uhttps://doi.org/10.4171/167
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/guedj_mini.jpg
942			_2EBK13878 _cEBK
999			_c50502 _d50502