Publisher:

Birkhäuser

Number of Pages:

439

Price:

79.95

ISBN:

978-0-8176-4537-3

Date Received:

Monday, May 21, 2007

Reviewable:

No

Reviewer Email Address:

Series:

Progress in Mathematics 261

Publication Date:

2007

Format:

Hardcover

Audience:

Category:

Monograph

Preface.

**Introduction.** Polynomial convexity. Uniform algebras. Plurisubharmonic fuctions. The Cauchy-Fantappiè Integral. The Oka—Weil Theorem. Some examples. Hulls with no analytic structure.-

**Some General Properties of Polynomially Convex Sets.** Applications of the Cousin problems. Two characterizations of polynomially convex sets. Applications of Morse theory and algebraic topology. Convexity in Stein manifolds.-

**Sets of Finite Length.** Introduction. One-dimensional varieties. Geometric preliminaries. Function-theoretic preliminaries. Subharmonicity results. Analytic structure in hulls. Finite area. The continuation of varieties.-

**Sets of Class A _{1}.** Introductory remarks. Measure-theoretic preliminaries. Sets of class A

**Further Results.** Isoperimetry. Removable singularities. Surfaces in strictly pseudoconvex boundaries.-

**Approximation.** Totally real manifolds. Holomorphically convex sets. Approximation on totally real manifolds. Some tools from rational approximation. Algebras on surfaces. Tangential approximation.-

**Varieties in Strictly Pseudoconvex Domains.** Interpolation. Boundary regularity. Uniqueness.-

**Examples and Counter Examples.** Unions of planes and balls. Pluripolar graphs. Deformations. Sets with symmetry.-

Bibliography. Index.

Publish Book:

Modify Date:

Monday, May 21, 2007

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