Archive for Rational Mechanics and Analysis

, Volume 229, Issue 3, pp 1015–1035 | Cite as

The Exponential Map of the Group of Area-Preserving Diffeomorphisms of a Surface with Boundary

  • James Benn
  • Gerard Misiołek
  • Stephen C. Preston


We prove that the Riemannian exponential map of the right-invariant L2 metric on the group of volume-preserving diffeomorphisms of a two-dimensional manifold with a nonempty boundary is a nonlinear Fredholm map of index zero.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Massey University, Palmerston NorthPalmerston NorthNew Zealand
  2. 2.Department of MathematicsNotre Dame UniversityNotre DameUSA
  3. 3.Department of MathematicsBrooklyn College and CUNY Graduate CenterBrooklynUSA

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