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Kähler-Einstein metrics singular along a smooth divisor

Raffe Mazzeo (1999)

Journées équations aux dérivées partielles

In this note 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 shall 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...

Kähler-Hodge Theory for Conformal Complex Cones.

J. Brüning, M. Lesch (1993)

Geometric and functional analysis

Kashaev's conjecture and the Chern-Simons invariants of knots and links.

Murakami, Hitoshi, Kurakami, Jun, Okamoto, Miyuki, Takata, Toshie, Yokota, Yoshiyuki (2002)

Experimental Mathematics

Kreisscheiben auf Riemannschen Flächen und Eigenwerte des Laplace-Operators.

Heinz Huber (1993)

Journal für die reine und angewandte Mathematik

K-theory from the point of view of C*-algebras and Fredholm representations

Alexandr Mishchenko (2005)

Open Mathematics

These notes represent the subject of five lectures which were delivered as a minicourse during the VI conference in Krynica, Poland, “Geometry and Topology of Manifolds”, May, 2–8, 2004.

K-theory of Boutet de Monvel's algebra

Severino T. Melo, Ryszard Nest, Elmar Schrohe (2003)

Banach Center Publications

We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).