Viscosity solutions to degenerate Complex Monge-Ampère equations

Abstract

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.

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• The Hölder continuous subsolution theorem for complex Hessian equations
• Convergence of the weak Kähler-Ricci Flow on manifolds of general type
• Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights
• $C^{1,1}$ regularity of degenerate complex Monge-Ampère equations and some applications