Viscosity solutions to degenerate Complex Monge-Ampère equations

Philippe Eyssidieux (1) , Vincent Guedj (2) , Ahmed Zeriahi (3)

1 IF - Institut Fourier
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We develop an alternative approach to Degenerate complex Monge-Ampère equations on compact Kähler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. We generalize to the Kähler case a theorem due to Dinew and Zhang in the projective case to the effect that their pluripotential solutions constructed previously by the authors are continuous.

Mots clés: Complex Monge-Ampère equations: Viscosity solutions: Pluripotential theory: Compact Kähler Manifolds

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

Philippe Eyssidieux, Vincent Guedj, Ahmed Zeriahi. Viscosity solutions to degenerate Complex Monge-Ampère equations. Communications on Pure and Applied Mathematics, 2011, 64 (8), pp.1059--1094. ⟨10.1002/cpa.20364⟩. ⟨hal-00496620⟩