30Cxx Geometric function theory
This subtopic studies geometric function theory, emphasizing conformal maps, univalent functions, and the geometric structure of holomorphic mappings.
Specific topics
30C10 Polynomials and rational functions of one complex variable
Overview
30C10 studies polynomials and rational functions of one complex variable in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for polynomials and rational functions of one complex variable
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C15 Zeros of polynomials, rational functions, and other analytic functions
Overview
30C15 studies zeros of polynomials, rational functions, and other analytic functions in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for zeros of polynomials, rational functions, and other analytic functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C20 Conformal mappings of special domains
Overview
30C20 studies conformal mappings of special domains in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for conformal mappings of special domains
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C25 Covering theorems in conformal mapping theory
Overview
30C25 studies covering theorems in conformal mapping theory in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for covering theorems in conformal mapping theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C30 Numerical methods in conformal mapping theory
Overview
30C30 studies numerical methods in conformal mapping theory in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for numerical methods in conformal mapping theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C35 General theory of conformal mappings
Overview
30C35 studies general theory of conformal mappings in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general theory of conformal mappings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C40 Kernel functions and applications in conformal mapping
Overview
30C40 studies kernel functions and applications in conformal mapping in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for kernel functions and applications in conformal mapping
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C45 Special classes of univalent and multivalent functions
Overview
30C45 studies special classes of univalent and multivalent functions in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for special classes of univalent and multivalent functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C50 Coefficient problems for univalent and multivalent functions
Overview
30C50 studies coefficient problems for univalent and multivalent functions in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for coefficient problems for univalent and multivalent functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C55 General theory of univalent and multivalent functions
Overview
30C55 studies general theory of univalent and multivalent functions in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general theory of univalent and multivalent functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C62 Quasiconformal mappings in the complex plane
Overview
30C62 studies quasiconformal mappings in the complex plane in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for quasiconformal mappings in the complex plane
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C65 Quasiconformal mappings in $\mathbb{R}^n$
Overview
30C65 studies quasiconformal mappings in $\mathbb{r}^n$ in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for quasiconformal mappings in $\mathbb{r}^n$
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C70 Extremal problems for conformal and quasiconformal mappings
Overview
30C70 studies extremal problems for conformal and quasiconformal mappings in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for extremal problems for conformal and quasiconformal mappings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C75 Extremal problems for conformal mappings
Overview
30C75 studies extremal problems for conformal mappings in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for extremal problems for conformal mappings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C80 Maximum principle, Schwarz lemma, Phragmén-Lindelöf principle
Overview
30C80 studies maximum principle, schwarz lemma, phragmã©n-lindelã¶f principle in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for maximum principle, schwarz lemma, phragmã©n-lindelã¶f principle
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks
30C85 Capacity and harmonic measure in the complex plane
Overview
30C85 studies capacity and harmonic measure in the complex plane in geometric function theory. It studies geometric and conformal properties of analytic functions, including univalence, distortion, and mapping behavior.
Related Wikipedia Page
Geometric Function Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for capacity and harmonic measure in the complex plane
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to analyze conformal maps, distortion estimates, and boundary phenomena.
Applications
- Conformal mapping
- Univalent function theory
- Boundary behavior and distortion
References
Recommended Textbooks