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Inventiones mathematicae

, Volume 113, Issue 1, pp 511–529 | Cite as

A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus

  • A. M. Bloch
  • H. Flaschka
  • T. Ratiu
Article

Summary

The group of area preserving diffeomorphisms of the annulus acts on its Lie algebra, the globally Hamiltonian vectorfields on the annulus. We consider a certain Hilbert space completion of this group (thinking of it as a group of unitary operators induced by the diffeomorphisms), and prove that the projection of an adjoint orbit onto a “Cartan” subalgebra isomorphic toL2 ([0, 1]) is an infinite-dimensional, weakly compact, convex set, whose extreme points coincide with the orbit, through a certain function, of the “permutation” semigroup of measure preserving transformations of [0, 1].

Keywords

Hilbert Space Extreme Point Unitary Operator Measure Preserve Area Preserve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • A. M. Bloch
    • 1
  • H. Flaschka
    • 2
  • T. Ratiu
    • 3
  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Department of MathematicsThe University of ArizonaTucsonUSA
  3. 3.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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