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Geometry
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Mathematical Subject Classification – MSC2010
31-XX
Potential theory
[For probabilistic potential theory, see
60J45
]
16166
31-00
General reference works
(handbooks, dictionaries, bibliographies, etc.)
10
31-01
Instructional exposition
(textbooks, tutorial papers, etc.)
62
31-02
Research exposition
(monographs, survey articles)
206
31-03
Historical
(must also be assigned at least one classification number from Section
01
)
50
31-04
Explicit machine computation and programs
(not the theory of computation or programming)
12
31-06
Proceedings, conferences, collections, etc.
127
31Axx
Two-dimensional theory
5412
31A05
Harmonic, subharmonic, superharmonic functions
1777
31A10
Integral representations, integral operators, integral equations methods
684
31A15
Potentials and capacity, harmonic measure, extremal length
[See also
30C85
]
1152
31A20
Boundary behavior
(theorems of Fatou type, etc.)
377
31A25
Boundary value and inverse problems
834
31A30
Biharmonic, polyharmonic functions and equations, Poisson’s equation
998
31A35
Connections with differential equations
210
31A99
None of the above, but in this section
174
31Bxx
Higher-dimensional theory
6326
31B05
Harmonic, subharmonic, superharmonic functions
2117
31B10
Integral representations, integral operators, integral equations methods
1025
31B15
Potentials and capacities, extremal length
1316
31B20
Boundary value and inverse problems
905
31B25
Boundary behavior
818
31B30
Biharmonic and polyharmonic equations and functions
764
31B35
Connections with differential equations
416
31B99
None of the above, but in this section
192
31Cxx
Other generalizations
4830
31C05
Harmonic, subharmonic, superharmonic functions
888
31C10
Pluriharmonic and plurisubharmonic functions
[See also
32U05
]
643
31C12
Potential theory on Riemannian manifolds
[See also
53C20
; for Hodge theory, see
58A14
]
432
31C15
Potentials and capacities
842
31C20
Discrete potential theory and numerical methods
361
31C25
Dirichlet spaces
1021
31C35
Martin boundary theory
[See also
60J50
]
289
31C40
Fine potential theory
111
31C45
Other generalizations
(nonlinear potential theory, etc.)
508
31C99
None of the above, but in this section
271
31Dxx
Axiomatic potential theory
972
31D05
Axiomatic potential theory
972
31D99
None of the above, but in this section
0
31Exx
Potential theory on metric spaces
66
31E05
Potential theory on metric spaces
64
31E99
None of the above, but in this section
1
Overview
00
General mathematics
01
History; biography
03
Mathematical logic
05
Combinatorics
06
Ordered structures
08
General algebraic systems
11
Number theory
12
Field theory and polynomials
13
Commutative algebra
14
Algebraic geometry
15
Linear and multilinear algebra; matrix theory
16
Associative rings and algebras
17
Nonassociative rings and algebras
18
Category theory, homological algebra
19
$K$-theory
20
Group theory and generalizations
22
Topological groups, Lie groups
26
Real functions
28
Measure and integration
30
Functions of a complex variable
31
Potential theory
32
Functions of several complex variables and analytic spaces
33
Special functions
34
Ordinary differential equations (ODE)
35
Partial differential equations (PDE)
37
Dynamical systems and ergodic theory
39
Difference and functional equations
40
Sequences, series, summability
41
Approximation and expansions
42
Fourier analysis
43
Abstract harmonic analysis
44
Integral transforms, operational calculus
45
Integral equations
46
Functional analysis
47
Operator theory
49
Calculus of variations and optimal control; optimization
51
Geometry
52
Convex and discrete geometry
53
Differential geometry
54
General topology
55
Algebraic topology
57
Manifolds and cell complexes
58
Global analysis, analysis on manifolds
60
Probability theory and stochastic processes
62
Statistics
65
Numerical analysis
68
Computer science
70
Mechanics of particles and systems
74
Mechanics of deformable solids
76
Fluid mechanics
78
Optics, electromagnetic theory
80
Classical thermodynamics, heat transfer
81
Quantum Theory
82
Statistical mechanics, structure of matter
83
Relativity and gravitational theory
85
Astronomy and astrophysics
86
Geophysics
90
Optimization
91
Game theory, economics, social and behavioral sciences
92
Applications of mathematics to Biology and other natural sciences
93
Systems theory; control
94
Information and communication, circuits
97
Mathematics education
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