Analyticity of sets associated to Lelong numbers and the extension of closed positive currents
- Y. Siu
- Mathematics
- 1 March 1974
Invariance of plurigenera
- Y. Siu
- Mathematics
- 15 December 1997
In this paper we give a proof of the following long conjectured result on the invariance of the plurigenera. Main Theorem. Let p : X ! D be a smooth projective family of compact complex manifolds…
Complex-analyticity of harmonic maps and strong rigidity of compact Kähler manifolds.
- Y. Siu
- MathematicsProceedings of the National Academy of Sciences…
- 1 May 1979
A harmonic map f between two compact Kähler manifolds is shown to be either holomorphic or conjugate holomorphic under a suitable negativity condition on the curvature of the image manifold and a…
Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics: Delivered At The German Mathematical Society Seminar In Düsseldorf In June, 1986
- Y. Siu
- Mathematics
- 1987
1. The heat equation approach to Hermitian-Einstein metrics on stable bundles.- 1. Definition of Hermitian-Einstein metrics.- 2. Gradient flow and the evolution equation.- 3. Existence of solution of…
Extension of Twisted Pluricanonical Sections with Plurisubharmonic Weight and Invariance of Semipositively Twisted Plurigenera for Manifolds Not Necessarily of General Type
- Y. Siu
- Mathematics
- 2002
Let X be a holomorphic family of compact complex projective algebraic manifolds with fibers X t over the open unit 1-disk Δ. Let \( K_{x_t } \) and K X be respectively the canonical line bundles of X…
Every Stein subvariety admits a Stein neighborhood
- Y. Siu
- History
- 1 February 1976
Hyperbolicity in Complex Geometry
- Y. Siu
- Mathematics
- 2004
A complex manifold is said to be hyperbolic if there exists no nonconstant holomorphic map from the affine complex line to it. We discuss the techniques and methods for the hyperbolicity problems for…
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