58XX 


Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46XX, 47Hxx, 53Cxx} {For geometric integration theory, see 49Q15]} 

58Jxx 

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


58J05 
Elliptic equations on manifolds, general theory [See also 35XX] 


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 
Etainvariants, ChernSimons 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] 


58J51 
Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity 


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. LieBäcklund) [See also 35A22] 


58J90 
Applications 


58J99 
None of the above, but in this section 