Abstract
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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Benn, J., Misiołek, G. & Preston, S.C. The Exponential Map of the Group of Area-Preserving Diffeomorphisms of a Surface with Boundary. Arch Rational Mech Anal 229, 1015–1035 (2018). https://doi.org/10.1007/s00205-018-1231-7
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DOI: https://doi.org/10.1007/s00205-018-1231-7