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Mathematical Sciences Classification System

58Jxx - Partial differential equations on manifolds; differential operators
[See also 32Wxx, 35-XX, 53Cxx]

• 9
  58J05
  Elliptic equations on manifolds, general theory [See also 35-XX]
• 2
  58J10
  Differential complexes [See also 35Nxx]; elliptic complexes
• 1
  58J15
  Relations with hyperfunctions
• 14
  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
• 6
  58J28
  Eta-invariants, Chern-Simons invariants
• 1
  58J30
  Spectral flows
• 9
  58J32
  Boundary value problems on manifolds
• 26
  58J35
  Heat and other parabolic equation methods
• 1
  58J37
  Perturbations; asymptotics
• 22
  58J40
  Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]
• 6
  58J42
  Noncommutative global analysis, noncommutative residues
• 12
  58J45
  Hyperbolic equations [See also 35Lxx]
• 58J47
  Propagation of singularities; initial value problems
• 23
  58J50
  Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
• 3
  58J51
  Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
• 3
  58J52
  Determinants and determinant bundles, analytic torsion
• 58J53
  Isospectrality
• 58J55
  Bifurcation [See also 35B32]
• 3
  58J60
  Relations with special manifold structures (Riemannian, Finsler, etc.)
• 16
  58J65
  Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
• 7
  58J70
  Invariance and symmetry properties [See also 35A30]
• 5
  58J72
  Correspondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]
• 58J90
  Applications
• 1
  58J99
  None of the above, but in this section