The exponential map of the group of area-preserving diffeomorphisms of a surface with boundary
classification
🧮 math.DG
keywords
boundarydiffeomorphismsexponentialgrouparea-preservingfredholmindexmanifold
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We prove that the Riemannian exponential map of the right-invariant $L^2$ 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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