Geometry of analytic continuation on complex manifolds -- history, survey, and report

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) The Levi problem (32E40) Domains of holomorphy (32T05)

Cites Work

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Suita conjecture and the Ohsawa-Takegoshi extension theorem
A proof of the Ohsawa-Takegoshi theorem with sharp estimates
Sur les domaines d'existence des fonctions de plusieurs variables complexes.
On the extension of $L^ 2$ holomorphic functions
A smooth pseudoconvex domain without pseudoconvex exhaustion
Variation of Bergman metrics on Riemann surfaces
Line bundle convexity of pseudoconvex domains in complex manifolds
Charakterisierung der Holomorphiegebiete durch die vollständige Kählersche Metrik
Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten
Subharmonicity properties of the Bergman kernel and some other functions associated to pseudoconvex domains
Locally Stein domains over holomorphically convex manifolds
On the neighborhood of a compact complex curve with topologically trivial normal bundle
Strongly pseudoconvex manifolds and strongly pseudoconvex domains
A counterexample to the Serre problem with a bounded domain of ${\mathbb{C}}^ 2$ as fiber
Harmonic mappings and disc bundles over compact Kähler manifolds
On Levi's problem and the imbedding of real-analytic manifolds
Projective manifolds with ample tangent bundles
Finiteness theorems on weakly 1-complete manifolds
Compact Kähler manifolds of positive bisectional curvature
Pseudoconvex domains over Grassmann manifolds
Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay
Adjoint linear series on weakly 1-complete Kähler manifolds. I: Global projective embedding
Zur Theorie der Singularitäten der Funktionen mehrerer komplexen Veränderlichen. Regularitäts- und Konvergenzbereiche
Stein domains with Levi-plane boundaries on compact complex surfaces
A Stein domain with smooth boundary which has a product structure
An estimate for the Bergman distance on pseudoconvex domains
The Levi problem on projective manifolds
Linear Shafarevich conjecture
Generalizations of theorems of Nishino and Hartogs by the $L^2$ method
$L^2$ proof of Nishino's rigidity theorem
Variants of Hörmander's theorem on $q$-convex manifolds by a technique of infinitely many weights
A proof of Saitoh's conjecture for conjugate Hardy $H^2$ kernels
A solution of an $L^{2}$ extension problem with an optimal estimate and applications
The Levi problem for Riemann domains over Stein spaces with isolated singularities
On the equivalence of imbeddings of exceptional complex spaces
Domaines sans point critique interieur sur l'espace projectif complexe
Domaines pseudoconvexes infinis et la métrique riemannienne dans un espace projectif
Bemerkenswerte pseudokonvexe Mannigfaltigkeiten
$L^ 2$ estimates and existence theorems for the $\partial$-operator
Über Modifikationen und exzeptionelle analytische Mengen
Algebraic approximation of structures over complete local rings
Über die konforme Abbildung eines veränderlichen Bereiches.
Resolution of singularities of an algebraic variety over a field of characteristic zero. I
A sharp effectiveness result of Demailly's strong openness conjecture
On the Levi problem on Kähler manifolds under the negativity of canonical bundles on the boundary
Positivity of twisted relative pluricanonical bundles and their direct images
Théorèmes de finitude pour la cohomologie des espaces complexes
The Levi problem and the structure theorem for non-negatively curved complete Kähler manifolds
Ricci Curvature and Holomorphic Convexity in Kahler Manifolds
Estimations $\mathrm{L}^2$ pour l'opérateur $\bar \partial$ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète
The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
Some remarks on complex Lie groups
∂-cohomology and geometry of the boundary of pseudoconvex domains
Extension of holomorphic functions defined on non reduced analytic subvarieties
Bundle-convexity and Kernel asymptotics on a class of locally pseudoconvex domains

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