La Classification Mathématique par matières 2000
Mathematics subject Classification 2000

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58-XX Global analysis, analysis on manifolds [For geometric integration theory, see 49Q15]

• 58-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
• 58-01 Instructional exposition (textbooks, tutorial papers, etc.)
• 58-02 Research exposition (monographs, survey articles)
• 58-03 Historical (must also be assigned at least one classification number from Section 01)
• 58-04 Explicit machine computation and programs (not the theory of computation or programming)
• 58-06 Proceedings, conferences, collections, etc.
• 58-99 Global analysis, analysis on manifolds (not classified at a more specific level)
• 58Axx General theory of differentiable manifolds [See also 32Cxx]
• 58Bxx Infinite-dimensional manifolds
• 58Cxx Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]
• 58Dxx Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]
• 58Exx Variational problems in infinite-dimensional spaces
  • 58E05 Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)
  • 58E07 Abstract bifurcation theory
  • 58E09 Group-invariant bifurcation theory
  • 58E10 Applications to the theory of geodesics (problems in one independent variable)
  • 58E11 Critical metrics
  • 58E12 Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
  • 58E15 Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
  • 58E17 Pareto optimality, etc., applications to economics [See also 90C29]
  • 58E20 Harmonic maps [See also 53C43], etc.
  • 58E25 Applications to control theory [See also 49-XX, 93-XX]
  • 58E30 Variational principles
  • 58E35 Variational inequalities (global problems)
  • 58E40 Group actions
  • 58E50 Applications
  • 58E99 None of the above, but in this section
• 58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
• 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]
• 58Kxx Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]
• 58Z05 Applications to physics

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