Complex Analysis

1. Front Matter

   Pages i-xx

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2. Oblique Polar Lines of ∫ _X |f|^2λ|g|^2μ□

   • D. Barlet, H.-M. Maire

   Pages 1-23

3. On Involutive Systems of First-order Nonlinear Partial Differential Equations

   • S. Berhanu

   Pages 25-50

4. Gevrey Hypoellipticity for an Interesting Variant of Kohn’s Operator

   • Antonio Bove, Marco Mughetti, David S. Tartakoff

   Pages 51-73

5. Subelliptic Estimates

   • David W. Catlin, John P. D’Angelo

   Pages 75-94

6. Invariant CR Mappings

   • John P. D’Angelo

   Pages 95-107

7. On the Subellipticity of Some Hypoelliptic Quasihomogeneous Systems of Complex Vector Fields

   • M. Derridj, B. Helffer

   Pages 109-123

8. Invariance of the Parametric Oka Property

   • Franc Forstnerič

   Pages 125-144

9. Positivity of the \( \bar \partial \)-Neumann Laplacian

   • Siqi Fu

   Pages 145-158

10. Compactness Estimates for the \( \bar \partial \)-Neumann Problem in Weighted L ²-spaces

    • Klaus Gansberger, Friedrich Haslinger

    Pages 159-174

11. Remarks on the Homogeneous Complex Monge-Ampère Equation

    • Pengfei Guan

    Pages 175-185

12. A Radó Theorem for Locally Solvable Structures of Co-rank One

    • J. Hounie

    Pages 187-203

13. Applications of a Parametric Oka Principle for Liftings

    • Finnur Lárusson

    Pages 205-211

14. Stability of the Vanishing of the \( \bar \partial _b \)-cohomoloy Under Small Horizontal Perturbations of the CR Structure in Compact Abstract q-concave CR Manifolds

    • Christine Laurent-Thiébaut

    Pages 213-225

15. Coherent Sheaves and Cohesive Sheaves

    • László Lempert

    Pages 227-244

16. Characteristic Classes of the Boundary of a Complex b-manifold

    • Gerardo A. Mendoza

    Pages 245-262

17. Solvability of Planar Complex Vector Fields with Applications to Deformation of Surfaces

    • Abdelhamid Meziani

    Pages 263-278

18. On the Zariski Closure of a Germ of Totally Geodesic Complex Submanifold on a Subvariety of a Complex Hyperbolic Space Form of Finite Volume

    • Ngaiming Mok

    Pages 279-300

19. The Large Time Asymptotics of the Entropy

    • Lei Ni

    Pages 301-306

20. The Closed Range Property for \( \bar \partial \) on Domains with Pseudoconcave Boundary

    • Mei-Chi Shaw

    Pages 307-320

This is a reference book for academics working in the fields of several complex variables, PDE theory and geometry. The book collects articles on most recent developments in these fields with special emphasis on interactions between them. It includes introductory and expository presentations of the relevant tools, techniques and objects for graduate and PhD students with a corresponding specialization. The volume comprises contributions of leading experts in the field written in a comprehensive and accessible style. Contributors: D. Barlet, S. Berhanu, A. Bove, D.W. Catlin, J.P. D’Angelo, M. Derridj, F. Forstnerič, S. Fu, K. Gansberger, P. Guan, F. Haslinger, B. Helffer, J. Hounie, N. Hungerbühler, F. Lárusson, Ch. Laurent-Thiébaut, L. Lempert, H.-M. Maire, G.A. Mendoza, A. Meziani, N. Mok, M. Mughetti L. Ni, M.-C. Shaw, D.S. Tartakoff, D. Zaitsev

• compactness
• complex analysis
• manifold
• manifolds
• operator
• singularities
• stability

• Department of Mathematics, University of California, San Diego (UCSD), La Jolla, USA

  Peter Ebenfelt

• Department of Mathematics, University of Fribourg, Fribourg, Switzerland

  Norbert Hungerbühler

• Department of Mathematics, Princeton, USA

  Joseph J. Kohn

• Department of Mathematics, The University of Hong Kong, Hong Kong SAR, China

  Ngaiming Mok

• Department of Mathematics, Texas A&M University, College Station, USA

  Emil J. Straube

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