Weak subsolutions to complex Monge-Ampère equations

Vincent Guedj (1) , Chinh H. Lu (2) , Ahmed Zeriahi (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UP11 UFR Sciences - Université Paris-Sud - Paris 11 - Faculté des Sciences

We compare various notions of weak subsolutions to degenerate complex Monge-Amp\`ere equations, showing that they all coincide. This allows us to give an alternative proof of mixed Monge-Amp\`ere inequalities due to Kolodziej and Dinew.

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Vincent Guedj, Chinh H. Lu, Ahmed Zeriahi. Weak subsolutions to complex Monge-Ampère equations. Journal of the Mathematical Society of Japan, 2019, ⟨10.2969/jmsj/79677967⟩. ⟨hal-01890196⟩