Cover

Title page

Contents

Preface

Polynomials on parabolic manifolds

1. Introduction

2. Parabolic manifolds

3. Aspects of pluripotential theory on 𝑆-parabolic manifolds

4. Example

5. Regular parabolic manifolds

References

Pseudoholomorphic discs and symplectic structures in Hilbert space

1. Introduction

2. Almost complex structures on Hilbert spaces

3. Some properties of the Cauchy integral

4. Local existence and regularity of pseudoholomorphic discs

5. Boundary value problems for 𝐽-holomorphic discs

6. Non-squeezing for symplectic transformations

7. Appendix I: Morrey’s embedding

8. Appendix II: Proof of Theorem 3.2

References

Pluripolarity of graphs of quasianalytic functions of several complex variables

1. Introduction

2. Preliminaries

3. Pluripolarity of graphs of Gonchar quasianalytic functions of several variables

4. Pluripolarity of graphs of algebroid functions

5. Pluripolarity of graphs of Denjoy quasianalytic functions of several variables

References

Lagrangian inclusion with an open Whitney umbrella is rationally convex

1. Introduction

2. Proof of Theorem 1

References

On systems of non-algebraic equations in ℂⁿ

Introduction

1. Preliminaries

2. Calculation of residue integrals

3. Power sums

4. Finding the sums of some multivariate series

References

Integral formulas for some matrix domains

1. Introduction

2. Results

3. Open problems

References

Nevanlinna’s characteristic functions with complex Hessian potential

1. Introduction

2. 𝑚-𝑠ℎ functions

3. Properties of the order function

4. Upper bounds for 𝑘 -order functions

References

Holomorphic continuation of functions in the domains with singular boundaries

References

Segre varieties and uniform estimates for harmonic functions

1. Introduction

2. Uniform estimates for harmonic functions

3. Proof of Theorem 1

References

Uniqueness property for Gonchar quasianalytic functions of several variables

1. Introduction

2. Main result

3. A theorem of Plesniak

Acknowledgement

References

Capacity dimension of the Perez-Marco set

1. Introduction

2. Main result

References

Analogue of the Lelong’s theorem for 𝑚-𝑤𝑠ℎ functions

Introduction

1. 𝑚-𝑤𝑠ℎ functions and their properties

2. A criteria of pluriharmonicity

References

Pluriregular compacts in ℙⁿ

Introduction

1. Quasiplurisubharmonic functions

2. Green function and pluriregularity in ℙⁿ

3. Appendix. Pluriregularity of the Julia set

References

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