Ebook: Complex Analysis and Geometry: International Conference in Honor of Pierre Lelong

This collection of 18 research papers, dedicated to Pierre Lelong, describes the state of the art on representative problems of complex analysis and geometry. The book opens with an exposition of the achievements of Pierre Lelong on plurisubharmonic functions, closed positive currents, and their further study by other mathematicians. Moreover, a list of eleven open problems is given. All other contributions contain new results related, for example, to the following items: - Capacities, product of positive currents, L2 extension theorems, Bergman kernels and metrics, new properties of convex domains of finite type - Non-compact boundaries of Levi-flat hypersurfaces of C2, compact boundary problems as application of compactly supported measures orthogonal to polynomials, Hartogs' theorem on some open subsets of a projective manifold, Malgrange vanishing theorem with support conditions - Embeddings for 3-dimensional CR-manifolds, geometrization of hypoellipticity, stationary complex curves and complete integrability - Regular polynomial mappings of Ck in complex dynamics, a direct proof of the density of repulsive cycles in the Julia set. The book is aimed at researchers and advanced graduate students in complex and real analysis, algebraic geometry and number theory.

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This collection of 18 research papers, dedicated to Pierre Lelong, describes the state of the art on representative problems of complex analysis and geometry. The book opens with an exposition of the achievements of Pierre Lelong on plurisubharmonic functions, closed positive currents, and their further study by other mathematicians. Moreover, a list of eleven open problems is given. All other contributions contain new results related, for example, to the following items: - Capacities, product of positive currents, L2 extension theorems, Bergman kernels and metrics, new properties of convex domains of finite type - Non-compact boundaries of Levi-flat hypersurfaces of C2, compact boundary problems as application of compactly supported measures orthogonal to polynomials, Hartogs' theorem on some open subsets of a projective manifold, Malgrange vanishing theorem with support conditions - Embeddings for 3-dimensional CR-manifolds, geometrization of hypoellipticity, stationary complex curves and complete integrability - Regular polynomial mappings of Ck in complex dynamics, a direct proof of the density of repulsive cycles in the Julia set. The book is aimed at researchers and advanced graduate students in complex and real analysis, algebraic geometry and number theory.
Content:
Front Matter....Pages i-xiv
Pr?sence de I’oeuvre de Pierre Lelong dans les grands th?mes de recherches d’aujourd’hui....Pages 1-37
Wiener’s type sufficient conditions for regularity in ? N ....Pages 39-46
On the Ohsawa-Takegoshi-Manivel L 2 extension theorem....Pages 47-82
A geometrical application of the product of two positive currents....Pages 83-90
Hypoellipticity: Geometrization and speculation....Pages 91-109
Moment problems for weighted Bergman kernels....Pages 111-122
On the Bergman metric near a plurisubharmonic barrier point....Pages 123-132
On the vanishing order of a holomorphic germ along a complex analytic germ in ? n ....Pages 133-142
Stationary curves and complete integrability in the complex domain....Pages 143-150
The Malgrange vanishing theorem with support conditions....Pages 151-162
Mesures orthogonales `support compact de longueur finie et applications....Pages 163-172
Convexity and Hartogs’s theorem in some open subset of a projective manifold....Pages 173-181
Pointwise nonisotropic support functions on convex domains....Pages 183-192
Un exemple d’obstruction g?om?trique `l’extension des fonctions holomorphes born?es....Pages 193-201
Potential theory in complex dynamics: Regular polynomial mappings of C k ....Pages 203-211
Boundaries of Levi-flat hypersurfaces of ?2 ....Pages 213-219
Une d?monstration directe de la densit? des cycles r?pulsifs dans l’ensemble de Julia....Pages 221-222
Embeddings for 3-dimensional CR-manifolds....Pages 223-236
Back Matter....Pages 237-241

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This collection of 18 research papers, dedicated to Pierre Lelong, describes the state of the art on representative problems of complex analysis and geometry. The book opens with an exposition of the achievements of Pierre Lelong on plurisubharmonic functions, closed positive currents, and their further study by other mathematicians. Moreover, a list of eleven open problems is given. All other contributions contain new results related, for example, to the following items: - Capacities, product of positive currents, L2 extension theorems, Bergman kernels and metrics, new properties of convex domains of finite type - Non-compact boundaries of Levi-flat hypersurfaces of C2, compact boundary problems as application of compactly supported measures orthogonal to polynomials, Hartogs' theorem on some open subsets of a projective manifold, Malgrange vanishing theorem with support conditions - Embeddings for 3-dimensional CR-manifolds, geometrization of hypoellipticity, stationary complex curves and complete integrability - Regular polynomial mappings of Ck in complex dynamics, a direct proof of the density of repulsive cycles in the Julia set. The book is aimed at researchers and advanced graduate students in complex and real analysis, algebraic geometry and number theory.
Content:
Front Matter....Pages i-xiv
Pr?sence de I’oeuvre de Pierre Lelong dans les grands th?mes de recherches d’aujourd’hui....Pages 1-37
Wiener’s type sufficient conditions for regularity in ? N ....Pages 39-46
On the Ohsawa-Takegoshi-Manivel L 2 extension theorem....Pages 47-82
A geometrical application of the product of two positive currents....Pages 83-90
Hypoellipticity: Geometrization and speculation....Pages 91-109
Moment problems for weighted Bergman kernels....Pages 111-122
On the Bergman metric near a plurisubharmonic barrier point....Pages 123-132
On the vanishing order of a holomorphic germ along a complex analytic germ in ? n ....Pages 133-142
Stationary curves and complete integrability in the complex domain....Pages 143-150
The Malgrange vanishing theorem with support conditions....Pages 151-162
Mesures orthogonales `support compact de longueur finie et applications....Pages 163-172
Convexity and Hartogs’s theorem in some open subset of a projective manifold....Pages 173-181
Pointwise nonisotropic support functions on convex domains....Pages 183-192
Un exemple d’obstruction g?om?trique `l’extension des fonctions holomorphes born?es....Pages 193-201
Potential theory in complex dynamics: Regular polynomial mappings of C k ....Pages 203-211
Boundaries of Levi-flat hypersurfaces of ?2 ....Pages 213-219
Une d?monstration directe de la densit? des cycles r?pulsifs dans l’ensemble de Julia....Pages 221-222
Embeddings for 3-dimensional CR-manifolds....Pages 223-236
Back Matter....Pages 237-241
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