32Hxx Holomorphic mappings
This subtopic studies holomorphic mappings, including mapping problems, extension phenomena, and qualitative properties of complex-analytic maps.
Specific topics
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions
Overview
32H02 studies holomorphic mappings, (holomorphic) embeddings and related questions in holomorphic mappings. It studies holomorphic maps between complex spaces, including local mapping behavior, fibers, and extension phenomena.
Related Wikipedia Page
Holomorphic Mappings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for holomorphic mappings, (holomorphic) embeddings and related questions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in complex geometry, mapping problems, and analytic continuation.
Applications
- Mapping and fiber structure
- Holomorphic extension
- Complex analytic embeddings
References
Recommended Textbooks
32H04 Meromorphic mappings in several complex variables
Overview
32H04 studies meromorphic mappings in several complex variables in holomorphic mappings. It studies holomorphic maps between complex spaces, including local mapping behavior, fibers, and extension phenomena.
Related Wikipedia Page
Holomorphic Mappings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for meromorphic mappings in several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in complex geometry, mapping problems, and analytic continuation.
Applications
- Mapping and fiber structure
- Holomorphic extension
- Complex analytic embeddings
References
Recommended Textbooks
32H25 Picard-type theorems and generalizations for several complex variables
Overview
32H25 studies picard-type theorems and generalizations for several complex variables in holomorphic mappings. It studies holomorphic maps between complex spaces, including local mapping behavior, fibers, and extension phenomena.
Related Wikipedia Page
Holomorphic Mappings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for picard-type theorems and generalizations for several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in complex geometry, mapping problems, and analytic continuation.
Applications
- Mapping and fiber structure
- Holomorphic extension
- Complex analytic embeddings
References
Recommended Textbooks
32H30 Value distribution theory in higher dimensions
Overview
32H30 studies value distribution theory in higher dimensions in holomorphic mappings. It studies holomorphic maps between complex spaces, including local mapping behavior, fibers, and extension phenomena.
Related Wikipedia Page
Holomorphic Mappings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for value distribution theory in higher dimensions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in complex geometry, mapping problems, and analytic continuation.
Applications
- Mapping and fiber structure
- Holomorphic extension
- Complex analytic embeddings
References
Recommended Textbooks
32H35 Proper mappings, finiteness theorems
Overview
32H35 studies proper mappings, finiteness theorems in holomorphic mappings. It studies holomorphic maps between complex spaces, including local mapping behavior, fibers, and extension phenomena.
Related Wikipedia Page
Holomorphic Mappings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for proper mappings, finiteness theorems
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in complex geometry, mapping problems, and analytic continuation.
Applications
- Mapping and fiber structure
- Holomorphic extension
- Complex analytic embeddings
References
Recommended Textbooks
32H40 Boundary regularity of mappings in several complex variables
Overview
32H40 studies boundary regularity of mappings in several complex variables in holomorphic mappings. It studies holomorphic maps between complex spaces, including local mapping behavior, fibers, and extension phenomena.
Related Wikipedia Page
Holomorphic Mappings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for boundary regularity of mappings in several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in complex geometry, mapping problems, and analytic continuation.
Applications
- Mapping and fiber structure
- Holomorphic extension
- Complex analytic embeddings
References
Recommended Textbooks
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps
Overview
32H50 studies iteration of holomorphic maps, fixed points of holomorphic maps in holomorphic mappings. It studies holomorphic maps between complex spaces, including local mapping behavior, fibers, and extension phenomena.
Related Wikipedia Page
Holomorphic Mappings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for iteration of holomorphic maps, fixed points of holomorphic maps
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in complex geometry, mapping problems, and analytic continuation.
Applications
- Mapping and fiber structure
- Holomorphic extension
- Complex analytic embeddings
References
Recommended Textbooks