32-XX 
|
Several complex variables and analytic spaces
{For infinite-dimensional holomorphy, see also
46G20 ,
58B12 }
|
|
32-00
|
General reference works (handbooks, dictionaries, bibliographies, etc.)
|
|
32-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
|
|
32-02
|
Research exposition (monographs, survey articles)
|
|
32-03
|
Historical {!must also be assigned at least one classification number from section 01}
|
|
32-04
|
Explicit machine computation and programs (not the theory of computation or programming)
|
|
32-06
|
Proceedings, conferences, collections, etc.
|
|
32Axx
|
Holomorphic functions of several complex variables
|
|
32A05
|
Power series, series of functions
|
|
32A07
|
Special domains (Reinhardt, Hartogs, circular, tube)
|
|
32A10
|
Holomorphic functions
|
|
32A12
|
Multifunctions
|
|
32A15
|
Entire functions
|
|
32A17
|
Special families of functions
|
|
32A18
|
Bloch functions, normal functions
|
|
32A19
|
Normal families of functions, mappings
|
|
32A20
|
Meromorphic functions
|
|
32A22
|
Nevanlinna theory (local); growth estimates; other inequalities
{For geometric theory, see
32H25 ,
32H30 }
|
|
32A25
|
Integral representations; canonical kernels (Szeg\"o, Bergman, etc.)
|
|
32A26
|
Integral representations, constructed kernels (e.g. Cauchy, Fantappi\`e-type kernels)
|
|
32A27
|
Local theory of residues
[See also
32C30 ]
|
|
32A30
|
Other generalizations of function theory of one complex variable {!should also be assigned at least one classification number from section 30}
{For functions of several hypercomplex variables, see
30G35 }
|
|
32A35
|
$H^p$-spaces, Nevanlinna spaces
[See also
32M15 ,
42B30 ,
43A85 ,
46J15 ]
|
|
32A36
|
Bergman spaces
|
|
32A37
|
Other spaces of holomorphic functions (e.g.
Bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)
[See also
46Exx ]
|
|
32A38
|
Algebras of holomorphic functions
[See also
30H05 ,
46J10 ,
46J15 ]
|
|
32A40
|
Boundary behavior of holomorphic functions
|
|
32A45
|
Hyperfunctions
[See also
46F15 ]
|
|
32A50
|
Harmonic analysis of several complex variables
[See mainly
43-XX ]
|
|
32A55
|
Singular integrals
|
|
32A60
|
Zero sets of holomorphic functions
|
|
32A65
|
Banach algebra techniques
[See mainly
46Jxx ]
|
|
32A70
|
Functional analysis techniques
[See mainly
46Exx ]
|
|
32A99
|
None of the above, but in this section
|
|
32Bxx
|
Local analytic geometry
[See also
13-XX
and
14-XX ]
|
|
32B05
|
Analytic algebras and generalizations, preparation theorems
|
|
32B10
|
Germs of analytic sets, local parametrization
|
|
32B15
|
Analytic subsets of affine space
|
|
32B20
|
Semi-analytic sets and subanalytic sets
[See also
14P15 ]
|
|
32B25
|
Triangulation and related questions
|
|
32B99
|
None of the above, but in this section
|
|
32Cxx
|
Analytic spaces
|
|
32C05
|
Real-analytic manifolds, real-analytic spaces
[See also
14Pxx ,
58A07 ]
|
|
32C07
|
Real-analytic sets, complex Nash functions
[See also
14P15 ,
14P20 ]
|
|
32C09
|
Embedding of real analytic manifolds
|
|
32C11
|
Complex supergeometry
[See also
14A22 ,
14M30 ,
58A50 ]
|
|
32C15
|
Complex spaces
|
|
32C18
|
Topology of analytic spaces
|
|
32C20
|
Normal analytic spaces
|
|
32C22
|
Embedding of analytic spaces
|
|
32C25
|
Analytic subsets and submanifolds
|
|
32C30
|
Integration on analytic sets and spaces, currents
{For local theory, see
32A25
or
32A27 }
|
|
32C35
|
Analytic sheaves and cohomology groups
[See also
14Fxx ,
18F20 ,
55N30 ]
|
|
32C36
|
Local cohomology of analytic spaces
|
|
32C37
|
Duality theorems
|
|
32C38
|
Sheaves of differential operators and their modules, D-modules
[See also
14F10 ,
16S32 ,
35A27 ,
58J15 ]
|
|
32C55
|
The Levi problem in complex spaces; generalizations
|
|
32C81
|
Applications to physics
|
|
32C99
|
None of the above, but in this section
|
|
32Dxx
|
Analytic continuation
|
|
32D05
|
Domains of holomorphy
|
|
32D10
|
Envelopes of holomorphy
|
|
32D15
|
Continuation of analytic objects
|
|
32D20
|
Removable singularities
|
|
32D25
|
Riemann domains
|
|
32D99
|
None of the above, but in this section
|
|
32Exx
|
Holomorphic convexity
|
|
32E05
|
Holomorphically convex complex spaces, reduction theory
|
|
32E10
|
Stein spaces, Stein manifolds
|
|
32E20
|
Polynomial convexity
|
|
32E30
|
Holomorphic and polynomial approximation, Runge pairs, interpolation
|
|
32E35
|
Global boundary behavior of holomorphic functions
|
|
32E40
|
The Levi problem
|
|
32E99
|
None of the above, but in this section
|
|
32Fxx
|
Geometric convexity
|
|
32F10
|
$Q$-convexity, $q$-concavity
|
|
32F17
|
Other notions of convexity
|
|
32F18
|
Finite-type conditions
|
|
32F27
|
Topological consequences of geometric convexity
|
|
32F32
|
Analytical consequences of geometric convexity (vanishing theorems, etc.)
|
|
32F45
|
Invariant metrics and pseudodistances
|
|
32F99
|
None of the above, but in this section
|
|
32Gxx
|
Deformations of analytic structures
|
|
32G05
|
Deformations of complex structures
[See also
13D10 ,
16S80 ,
58H10 ,
58H15 ]
|
|
32G07
|
Deformations of special (e.g. CR) structures
|
|
32G08
|
Deformations of fiber bundles
|
|
32G10
|
Deformations of submanifolds and subspaces
|
|
32G13
|
Analytic moduli problems
{For algebraic moduli problems, see
14D20 ,
14D22 ,
14H10 ,
14J10 }
[See also
14H15 ,
14J15 ]
|
|
32G15
|
Moduli of Riemann surfaces, Teichm\"uller theory
[See also
14H15 ,
30Fxx ]
|
|
32G20
|
Period matrices, variation of Hodge structure; degenerations
[See also
14D05 ,
14D07 ,
14K30 ]
|
|
32G34
|
Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation)
[See also
34Mxx ]
|
|
32G81
|
Applications to physics
|
|
32G99
|
None of the above, but in this section
|
|
32Hxx
|
Holomorphic mappings and correspondences
|
|
32H02
|
Holomorphic mappings, (holomorphic) embeddings and related questions
|
|
32H04
|
Meromorphic mappings
|
|
32H12
|
Boundary uniqueness of mappings
|
|
32H25
|
Picard-type theorems and generalizations
{For function-theoretic properties, see
32A22 }
|
|
32H30
|
Value distribution theory in higher dimensions
{For function-theoretic properties, see
32A22 }
|
|
32H35
|
Proper mappings, finiteness theorems
|
|
32H40
|
Boundary regularity of mappings
|
|
32H99
|
None of the above, but in this section
|
|
32Jxx
|
Compact analytic spaces
{For Riemann surfaces, see
14Hxx ,
30Fxx ;
for algebraic theory, see
14Jxx }
|
|
32J05
|
Compactification of analytic spaces
|
|
32J10
|
Algebraic dependence theorems
|
|
32J15
|
Compact surfaces
|
|
32J17
|
Compact $3$-folds
|
|
32J18
|
Compact $n$-folds
|
|
32J25
|
Transcendental methods of algebraic geometry
[See also
14C30 ]
|
|
32J27
|
Compact K\"ahler manifolds: generalizations, classification
|
|
32J81
|
Applications to physics
|
|
32J99
|
None of the above, but in this section
|
|
32Kxx
|
Generalizations of analytic spaces {!should also be assigned at least one other classification number from section 32 describing the type of problem}
|
|
32K05
|
Banach analytic spaces
[See also
58Bxx ]
|
|
32K07
|
Formal and graded complex spaces
[See also
58C50 ]
|
|
32K15
|
Differentiable functions on analytic spaces, differentiable spaces
[See also
58C25 ]
|
|
32K99
|
None of the above, but in this section
|
|
32Lxx
|
Holomorphic fiber spaces
[See also
55Rxx ]
|
|
32L05
|
Holomorphic bundles and generalizations
|
|
32L10
|
Sheaves and cohomology of sections of holomorphic vector bundles, general results
[See also
14F05 ,
18F20 ,
55N30 ]
|
|
32L15
|
Bundle convexity
[See also
32F10 ]
|
|
32L20
|
Vanishing theorems
|
|
32L25
|
Twistor theory, double fibrations
[See also
53C28 ]
|
|
32L81
|
Applications to physics
|
|
32L99
|
None of the above, but in this section
|
|
32Mxx
|
Complex spaces with a group of automorphisms
|
|
32M05
|
Complex Lie groups, automorphism groups acting on complex spaces
[See also
22E10 ]
|
|
32M10
|
Homogeneous complex manifolds
[See also
14M17 ,
57T15 ]
|
|
32M12
|
Almost homogeneous manifolds and spaces
[See also
14M17 ]
|
|
32M15
|
Hermitian symmetric spaces, bounded symmetric domains Jordan algebras
[See also
22E10 ,
22E40 ,
53C35 ,
57T15 ]
|
|
32M17
|
Automorphism groups of ${\bf C}^n$ and affine manifolds
|
|
32M25
|
Complex vector fields
|
|
32M99
|
None of the above, but in this section
|
|
32Nxx
|
Automorphic functions
[See also
11Fxx ,
20H10 ,
22E40 ,
30F35 ]
|
|
32N05
|
General theory of automorphic functions of several complex variables
|
|
32N10
|
Automorphic forms
|
|
32N15
|
Automorphic functions in symmetric domains
|
|
32N99
|
None of the above, but in this section
|
|
32P05
|
Non-Archimedean complex analysis {!should also be assigned at least one other classification number from section 32 describing the type of problem}
|
|
32Qxx
|
Complex manifolds
|
|
32Q05
|
Negative curvature manifolds
|
|
32Q10
|
Positive curvature manifolds
|
|
32Q15
|
K\"ahler manifolds
|
|
32Q20
|
K\"ahler-Einstein manifolds
[See also
53Cxx ]
|
|
32Q25
|
Calabi-Yau theory
|
|
32Q28
|
Stein manifolds
|
|
32Q30
|
Uniformization
|
|
32Q35
|
Complex manifolds as subdomains of Euclidean space
|
|
32Q40
|
Embedding theorems
|
|
32Q45
|
Hyperbolic and Kobayashi hyperbolic manifolds
|
|
32Q55
|
Topological aspects of complex manifolds
|
|
32Q57
|
Classification theorems
|
|
32Q60
|
Almost complex manifolds
|
|
32Q65
|
Pseudoholomorphic curves
|
|
32Q99
|
None of the above, but in this section
|
|
32Sxx
|
Singularities
|
|
32S05
|
Local singularities
[See also
14J17 ]
|
|
32S10
|
Invariants of analytic local rings
|
|
32S15
|
Equisingularity (topological and analytic)
[See also
14E15 ]
|
|
32S20
|
Global theory of singularities; cohomological properties
[See also
14E15 ]
|
|
32S22
|
Relations with arrangements of hyperplanes
[See also
52C30 ]
|
|
32S25
|
Surface and hypersurface singularities
[See also
14J17 ]
|
|
32S30
|
Deformations of singularities; vanishing cycles
[See also
14B07 ]
|
|
32S35
|
Mixed Hodge theory of singular varieties
[See also
14C30 ,
14D07 ]
|
|
32S40
|
Monodromy; relations with differential equations and $D$-modules
|
|
32S45
|
Modifications; resolution of singularities
[See also
14E15 ]
|
|
32S50
|
Topological aspects: Lefschetz theorems, topological classification, invariants
|
|
32S55
|
Milnor fibration; relations with knot theory
[See also
57M25 ,
57Q45 ]
|
|
32S60
|
Stratifications; constructible sheaves; intersection cohomology
[See also
58Kxx ]
|
|
32S65
|
Singularities of holomorphic vector fields and foliations
|
|
32S70
|
Other operations on singularities
|
|
32S99
|
None of the above, but in this section
|
|
32Txx
|
Pseudoconvex domains
|
|
32T05
|
Domains of holomorphy
|
|
32T15
|
Strongly pseudoconvex domains
|
|
32T20
|
Worm domains
|
|
32T25
|
Finite type domains
|
|
32T27
|
Geometric and analytic invariants on weakly pseudoconvex boundaries
|
|
32T35
|
Exhaustion functions
|
|
32T40
|
Peak functions
|
|
32T99
|
None of the above, but in this section
|
|
32Uxx
|
Pluripotential theory
|
|
32U05
|
Plurisubharmonic functions and generalizations
[See also
31C10 ]
|
|
32U10
|
Plurisubharmonic exhaustion functions
|
|
32U15
|
Pluripotential theory
|
|
32U20
|
Capacity theory and generalizations
|
|
32U25
|
Lelong numbers
|
|
32U30
|
Removable sets
|
|
32U35
|
Pluricomplex Green functions
|
|
32U40
|
Currents
|
|
32U99
|
None of the above, but in this section
|
|
32Vxx
|
$CR$ manifolds
|
|
32V05
|
$CR$ structures, $CR$ operators, and generalizations
|
|
32V10
|
$CR$ functions
|
|
32V15
|
$CR$ manifolds as boundaries of domains
|
|
32V20
|
Analysis on $CR$ manifolds
|
|
32V25
|
Extension of functions and other analytic objects from $CR$ manifolds
|
|
32V30
|
Embeddings of $CR$ manifolds
|
|
32V35
|
Finite type conditions on $CR$ manifolds
|
|
32V40
|
Real submanifolds in complex manifolds
|
|
32V99
|
None of the above, but in this section
|
|
32Wxx
|
Differential operators in several variables
|
|
32W05
|
$\Overline\partial$ and $\overline\partial$-Neumann operators
|
|
32W10
|
$\Overline\partial_b$ and $\overline\partial_b$-Neumann operators
|
|
32W20
|
Complex Monge-Amp\`ere operators
|
|
32W25
|
Pseudodifferential operators in several complex variables
|
|
32W30
|
Heat kernels in several complex variables
|
|
32W50
|
Other partial differential equations of complex analysis
|
|
32W99
|
None of the above, but in this section
|