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58Jxx - Partial differential equations on manifolds; differential operators

58J05 - Elliptic equations on manifolds, general theory
58J10 - Differential complexes ; elliptic complexes
58J15 - Relations with hyperfunctions
58J20 - Index theory and related fixed point theorems
58J22 - Exotic index theories
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
58J42 - Noncommutative global analysis, noncommutative residues
58J45 - Hyperbolic equations
58J47 - Propagation of singularities; initial value problems
58J50 - Spectral problems; spectral geometry; scattering theory
58J52 - Determinants and determinant bundles, analytic torsion
58J53 - Isospectrality
58J55 - Bifurcation
58J60 - Relations with special manifold structures (Riemannian, Finsler, etc.)
58J65 - Diffusion processes and stochastic analysis on manifolds
58J70 - Invariance and symmetry properties
58J72 - Correspondences and other transformation methods (e.g. Lie-Bäcklund)
58J90 - Applications
58J99 - Miscellaneous
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