Philippe Eyssidieux

Viscosity Solutions to Degenerate Complex Monge-Ampère Equations

We develop an alternative approach to Degenerate complex Monge-Ampere equations on compact Kahler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. We generalize to the Kahler 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.

Weak solutions to degenerate complex Monge–Ampère flows I

Studying the (long-term) behavior of the Kähler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge–Ampère equations. The purpose of this article, the first of a series on this subject, is to develop a viscosity theory for degenerate complex Monge–Ampère flows in domains of

Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

{\mathbb {C}}^n

Invariants de Von Neumann des faisceaux analytiques cohérents

Cn.

Singular Kähler-Einstein metrics

The (real) theory of fully non linear parabolic equations.- The KRF on positive Kodaira dimension Kahler manifolds.- The normalized Kahler-Ricci flow on Fano manifolds.- Bibliography.

Monge–Ampère equations in big cohomology classes

We extend to compact Kahler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach, based on an interversion lemma for fibrations with tori versus general type manifolds as fibers, gives a refinement of the classical work of Zuo. We extend to the Kahler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties

×Twhich we call the preferred Goldman-Millson isomorphism (definition 2.11). Themain theorem of [GolMil88] asserts that an abstract isomorphism between these twoformal germs exists. The original construction is not quite canonical, and we havetried to make the choices made there as explicit as possible. This is the rationalefor the length of section 2. It turns out that there is no good reason to give any kindof privilege to this preferred isomorphism. Two other very nice Goldman-Millson

SINGULAR K ¨ AHLER-EINSTEIN METRICS

Abstract. In order to study the group of