Skip to main content
Log in

Convexity properties of the moment mapping

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.


  1. Abraham, R., Marsden, J.: Foundations of mechanics. Reading, MA: Benjamin 1978

    Google Scholar 

  2. Arms, J., Marsden, J., Moncrief, V.: Symmetries and bifurcations of the momentum mapping. Commun. Math. Phys.78, 455–478 (1981)

    Google Scholar 

  3. Atiyah, M.: Convexity and commuting Hamiltonians. (preprint)

  4. Bott, R.: Non-degenerate critical manifolds. Ann. of Math.60, 248–261 (1954)

    Google Scholar 

  5. Heckman, G.: Projections of orbits and asymptotic behavior of multiplicities for compact Lie groups. (preprint)

  6. Humphreys, J.E.: Introduction to Lie algebras and representation theory. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  7. Kostant, B.: On convexity, the Weyl group and the Iwasawa decomposition. Ann. Sci. Ec. Norm. Sup.6, 413–455 (1973)

    Google Scholar 

  8. Kostant, B.: Quantization and unitary representations. In: Lecture Notes in Mathematics, Vol. 170. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  9. Marsden, J., Weinstein, A.: Reduction of symplectic manifolds with symmetry. Rep. Math. Phys.5, 121–130 (1974)

    Google Scholar 

  10. Montgomery, D., Samelson, H., Zippin, L.: Singular points of compact transformation groups. Ann. of Math. (2)63, 1–9 (1956)

    Google Scholar 

  11. Mostow, G.D.: On a conjecture of Montgomery. Ann. of Math. (2)65, 513–516 (1957)

    Google Scholar 

  12. Sternberg, S.: Lectures on differential geometry. Englewood Cliffs, NJ: Prentice-Hall 1964

    Google Scholar 

  13. Yang, C.-T.: On a problem of Montgomery, Proc. Am. Math. Soc.8, 255–275 (1957)

    Google Scholar 


  1. Guillemin, V., Sternberg, S.: Geometric quantization and multiplicities of group representations. Invent. Math. in press (1982)

  2. Heckman, G.: Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups. in press (1982)

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Guillemin, V., Sternberg, S. Convexity properties of the moment mapping. Invent Math 67, 491–513 (1982).

Download citation

  • Issue Date:

  • DOI: