Mathematics Branches, Topics, and Sub-Topics

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32Exx Holomorphic convexity

This subtopic studies holomorphic convexity, describing convexity properties in complex analysis and their consequences for function theory.

Specific topics

32E05 Holomorphically convex complex spaces

Overview

32E05 studies holomorphically convex complex spaces in holomorphic convexity. It studies holomorphic convexity, pseudoconvexity, and the approximation properties that drive Stein-space theory.

Related Wikipedia Page

Holomorphic Convexity (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for holomorphically convex complex spaces
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in several complex variables and complex geometry.

Applications

  • Stein spaces and domains of holomorphy
  • Approximation by holomorphic functions
  • Complex-geometric convexity

References

Recommended Textbooks

32E10 Stein spaces, Stein manifolds

Overview

32E10 studies stein spaces, stein manifolds in holomorphic convexity. It studies holomorphic convexity, pseudoconvexity, and the approximation properties that drive Stein-space theory.

Related Wikipedia Page

Holomorphic Convexity (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for stein spaces, stein manifolds
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in several complex variables and complex geometry.

Applications

  • Stein spaces and domains of holomorphy
  • Approximation by holomorphic functions
  • Complex-geometric convexity

References

Recommended Textbooks

32E20 Polynomial convexity

Overview

32E20 studies polynomial convexity in holomorphic convexity. It studies holomorphic convexity, pseudoconvexity, and the approximation properties that drive Stein-space theory.

Related Wikipedia Page

Holomorphic Convexity (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for polynomial convexity
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in several complex variables and complex geometry.

Applications

  • Stein spaces and domains of holomorphy
  • Approximation by holomorphic functions
  • Complex-geometric convexity

References

Recommended Textbooks

32E30 Holomorphic and polynomial approximation, Runge pairs, interpolation

Overview

32E30 studies holomorphic and polynomial approximation, runge pairs, interpolation in holomorphic convexity. It studies holomorphic convexity, pseudoconvexity, and the approximation properties that drive Stein-space theory.

Related Wikipedia Page

Holomorphic Convexity (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for holomorphic and polynomial approximation, runge pairs, interpolation
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in several complex variables and complex geometry.

Applications

  • Stein spaces and domains of holomorphy
  • Approximation by holomorphic functions
  • Complex-geometric convexity

References

Recommended Textbooks

32E35 Global boundary behavior of holomorphic functions

Overview

32E35 studies global boundary behavior of holomorphic functions in holomorphic convexity. It studies holomorphic convexity, pseudoconvexity, and the approximation properties that drive Stein-space theory.

Related Wikipedia Page

Holomorphic Convexity (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for global boundary behavior of holomorphic functions
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in several complex variables and complex geometry.

Applications

  • Stein spaces and domains of holomorphy
  • Approximation by holomorphic functions
  • Complex-geometric convexity

References

Recommended Textbooks

32E40 The Levi problem

Overview

32E40 studies the levi problem in holomorphic convexity. It studies holomorphic convexity, pseudoconvexity, and the approximation properties that drive Stein-space theory.

Related Wikipedia Page

Holomorphic Convexity (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for the levi problem
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in several complex variables and complex geometry.

Applications

  • Stein spaces and domains of holomorphy
  • Approximation by holomorphic functions
  • Complex-geometric convexity

References

Recommended Textbooks