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Title: Fractional Sobolev Metrics on Spaces of Immersed Curves
Authors: Bauer, M
Bruveris, M
Kolev, B
Keywords: Sobolev metrics of fractional order
Issue Date: 2017
Publisher: Springer-Verlag
Citation: Calculus of Variations and Partial Differential Equations, 2018, 57(1):27 (24 pp.)
Abstract: Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of smooth regular curves Imm(S1 , R 𝑑 ) and on its Sobolev completions ℐ π‘ž (S1 , R 𝑑 ). We prove local well-posedness of the geodesic equations both on the Banach manifold ℐ π‘ž (S1 , R 𝑑 ) and on the FrΒ΄echetmanifold Imm(S1 , R 𝑑 ) provided the order of the metric is greater or equal to one. In addition we show that the 𝐻𝑠 -metric induces a strong Riemannian metric on the Banach manifold ℐ 𝑠 (S1 , R 𝑑 ) of the same order 𝑠, provided 𝑠 > 3 2 . These investigations can be also interpreted as a generalization of the analysis for right invariant metrics on the diffeomorphism group.
ISSN: 0944-2669
Appears in Collections:Dept of Mathematics Research Papers

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