Plurisubharmonic envelopes and supersolutions
Guedj, Vincent ; Lu, Chinh H. ; Zeriahi, Ahmed
HAL, hal-01890198 / Harvested from HAL
Text on HAL
We make a systematic study of (quasi-)plurisubharmonic envelopes on compact K\"ahler manifolds, as well as on domains of $\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Amp\`ere equation. We use these ideas to solve complex Monge-Amp\`ere equations by taking lower envelopes of super-solutions.
Publié le : 2018-10-08
Classification:  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 
@article{hal-01890198,
     author = {Guedj, Vincent and Lu, Chinh H. and Zeriahi, Ahmed},
     title = {Plurisubharmonic envelopes and supersolutions},
     journal = {HAL},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01890198}
}

Guedj, Vincent; Lu, Chinh H.; Zeriahi, Ahmed. Plurisubharmonic envelopes and supersolutions. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01890198/