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

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-Bäcklund) [See also 35A22]
58J90 Applications
58J99 None of the above, but in this section