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Kähler-Einstein metrics singular along a smooth divisor. (English) Zbl 1009.32013
Journées “Équations aux dérivées partielles”, Saint-Jean-de-Monts, France, 31 mai au 4 juin 1999. Exposés Nos. I–XIX. Nantes: Université de Nantes. Exp. No. VI, 10 p. (1999).
Summary: We discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor \(D\). We begin with a general discussion of the problem, and give a rough outline of the ‘classical’ proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical or edge singularities and then some discussion of the new elements of the proof in this context.
For the entire collection see [Zbl 0990.00047].

32Q20 Kähler-Einstein manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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