|
58-XX
|
Global analysis, analysis on manifolds
[See also
32Cxx,
32Fxx,
46-XX,
47Hxx,
53Cxx]
{For geometric integration theory, see
49Q15}
|
|
58-00
|
General reference works (handbooks, dictionaries, bibliographies, etc.)
|
|
58-01
|
Instructional exposition (textbooks, tutorial papers, etc.)
|
|
58-02
|
Research exposition (monographs, survey articles)
|
|
58-03
|
Historical {!must also be assigned at least one classification number from section 01}
|
|
58-04
|
Explicit machine computation and programs (not the theory of computation or programming)
|
|
58-06
|
Proceedings, conferences, collections, etc.
|
|
58Axx
|
General theory of differentiable manifolds
|
|
58A03
|
Topos-theoretic approach to differentiable manifolds
|
|
58A05
|
Differentiable manifolds, foundations
|
|
58A07
|
Real-analytic and Nash manifolds
[See also
14P20,
32C07]
|
|
58A10
|
Differential forms
|
|
58A12
|
De_Rham theory
[See also
14Fxx]
|
|
58A14
|
Hodge theory
[See also
14C30,
14Fxx,
32J25,
32S35]
|
|
58A15
|
Exterior differential systems (Cartan theory)
|
|
58A17
|
Pfaffian systems
|
|
58A20
|
Jets
|
|
58A25
|
Currents
[See also
32C30,
53C65]
|
|
58A30
|
Vector distributions (subbundles of the tangent bundles)
|
|
58A32
|
Natural bundles
|
|
58A35
|
Stratified sets
[See also
32S60]
|
|
58A40
|
Differential spaces
|
|
58A50
|
Supermanifolds and graded manifolds
[See also
14A22,
32C11]
|
|
58A99
|
None of the above, but in this section
|
|
58Bxx
|
Infinite-dimensional manifolds
|
|
58B05
|
Homotopy and topological questions
|
|
58B10
|
Differentiability questions
|
|
58B12
|
Questions of holomorphy
[See also
32-XX,
46G20]
|
|
58B15
|
Fredholm structures
[See also
47A53]
|
|
58B20
|
Riemannian, Finsler and other geometric structures
[See also
53C20,
53C60]
|
|
58B25
|
Group structures and generalizations on infinite-dimensional manifolds
[See also
22E65,
58D05]
|
|
58B32
|
Geometry of quantum groups
|
|
58B34
|
Noncommutative geometry (\`a la Connes)
|
|
58B99
|
None of the above, but in this section
|
|
58Cxx
|
Calculus on manifolds; nonlinear operators
[See also
46Txx,
47Hxx]
|
|
58C05
|
Real-valued functions
|
|
58C06
|
Set valued and function-space valued mappings
[See also
47H04,
54C60]
|
|
58C07
|
Continuity properties of mappings
|
|
58C10
|
Holomorphic maps
[See also
32-XX]
|
|
58C15
|
Implicit function theorems; global Newton methods
|
|
58C20
|
Differentiation theory (Gateaux, Fr\'echet, etc.)
[See also
26Exx,
46G05]
|
|
58C25
|
Differentiable maps
|
|
58C30
|
Fixed point theorems on manifolds
[See also
47H10]
|
|
58C35
|
Integration on manifolds; measures on manifolds
[See also
28Cxx]
|
|
58C40
|
Spectral theory; eigenvalue problems
[See also
47J10,
58E07]
|
|
58C50
|
Analysis on supermanifolds or graded manifolds
|
|
58C99
|
None of the above, but in this section
|
|
58Dxx
|
Spaces and manifolds of mappings {!including nonlinear versions of
46Exx}
|
|
58D05
|
Groups of diffeomorphisms and homeomorphisms as manifolds
[See also
22E65,
57S05]
|
|
58D07
|
Groups and semigroups of nonlinear operators
[See also
17B65,
47H20]
|
|
58D10
|
Spaces of imbeddings and immersions
|
|
58D15
|
Manifolds of mappings
[See also
46T10,
54C35]
|
|
58D17
|
Manifolds of metrics (especially Riemannian)
|
|
58D19
|
Group actions and symmetry properties
|
|
58D20
|
Measures (Gaussian, cylindrical, etc.) on manifolds of maps
[See also
28Cxx,
46T12]
|
|
58D25
|
Equations in function spaces; evolution equations
[See also
34Gxx,
35K90,
35L90,
35R15,
37Lxx,
47Jxx]
|
|
58D27
|
Moduli problems for differential geometric structures
|
|
58D29
|
Moduli problems for topological structures
|
|
58D30
|
Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
|
|
58D99
|
None of the above, but in this section
|
|
58Exx
|
Variational problems in infinite-dimensional spaces
|
|
58E05
|
Abstract critical point theory (Morse theory, Ljusternik - Schnirelman (Lyusternik - Shnirel'man) theory, etc.)
|
|
58E07
|
Abstract bifurcation theory
|
|
58E09
|
Group-invariant bifurcation theory
|
|
58E10
|
Applications to the theory of geodesics (problems in one independent variable)
|
|
58E11
|
Critical metrics
|
|
58E12
|
Applications to minimal surfaces (problems in two independent variables)
[See also
49Q05]
|
|
58E15
|
Application to extremal problems in several variables; Yang - Mills functionals
[See also
81T13],
etc.
|
|
58E17
|
Pareto optimality, etc., applications to economics
[See also
90C29]
|
|
58E20
|
Harmonic maps
[See also
53C43],
etc.
|
|
58E25
|
Applications to control theory
[See also
49-XX,
93-XX]
|
|
58E30
|
Variational principles
|
|
58E35
|
Variational inequalities (global problems)
|
|
58E40
|
Group actions
|
|
58E50
|
Applications
|
|
58E99
|
None of the above, but in this section
|
|
58Hxx
|
Pseudogroups, differentiable groupoids and general structures on manifolds
|
|
58H05
|
Pseudogroups and differentiable groupoids
[See also
22A22,
22E65]
|
|
58H10
|
Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand - Fuks, etc.)
[See also
57R32]
|
|
58H15
|
Deformations of structures
[See also
32Gxx,
58J10]
|
|
58H99
|
None of the above, but in this section
|
|
58Jxx
|
Partial differential equations on manifolds
[See also
35-XX]
|
|
58J05
|
Elliptic equations on manifolds, general theory
[See also
35-XX]
|
|
58J10
|
Differential complexes
[See also
35Nxx];
elliptic complexes
|
|
58J15
|
Relations with hyperfunctions
|
|
58J20
|
Index theory and related fixed point theorems
[See also
19K56,
46L80]
|
|
58J22
|
Exotic index theories
[See also
19K56,
46L05,
46L10,
46L80,
46M20]
|
|
58J26
|
Elliptic genera
|
|
58J28
|
Eta-invariants, Chern - Simons invariants
|
|
58J30
|
Spectral flows
|
|
58J32
|
Boundary value problems on manifolds
|
|
58J35
|
Heat and other parabolic equation methods
|
|
58J37
|
Perturbations; asymptotics
|
|
58J40
|
Pseudodifferential and Fourier integral operators on manifolds
[See also
35Sxx]
|
|
58J42
|
Noncommutative global analysis, noncommutative residues
|
|
58J45
|
Hyperbolic equations
[See also
35Lxx]
|
|
58J47
|
Propagation of singularities; initial value problems
|
|
58J50
|
Spectral problems; spectral geometry; scattering theory
[See also
35Pxx]
|
|
58J52
|
Determinants and determinant bundles, analytic torsion
|
|
58J53
|
Isospectrality
|
|
58J55
|
Bifurcation
[See also
35B32]
|
|
58J60
|
Relations with special manifold structures (Riemannian, Finsler, etc.)
|
|
58J65
|
Diffusion processes and stochastic analysis on manifolds
[See also
35R60,
60H10,
60J60]
|
|
58J70
|
Invariance and symmetry properties
[See also
35A30]
|
|
58J72
|
Correspondences and other transformation methods (e.g. Lie - B\"acklund)
[See also
35A22]
|
|
58J90
|
Applications
|
|
58J99
|
None of the above, but in this section
|
|
58Kxx
|
Theory of singularities and catastrophe theory
[See also
37-XX]
|
|
58K05
|
Critical points of functions and mappings
|
|
58K10
|
Monodromy
|
|
58K15
|
Topological properties of mappings
|
|
58K20
|
Algebraic and analytic properties of mappings
|
|
58K25
|
Stability
|
|
58K30
|
Global theory
|
|
58K35
|
Catastrophe theory
|
|
58K40
|
Classification; finite determinacy of map germs
|
|
58K45
|
Singularities of vector fields, topological aspects
|
|
58K50
|
Normal forms
|
|
58K55
|
Asymptotic behavior
|
|
58K60
|
Deformation of singularities
|
|
58K65
|
Topological invariants
|
|
58K70
|
Symmetries, equivariance
|
|
58K99
|
None of the above, but in this section
|
|
58Z05
|
Applications to physics
|