Geodesic Completeness for Sobolev $H^s$-metrics on the Diffeomorphisms Group of the Circle

Abstract

We prove that the weak Riemannian metric induced by the fractional Sobolev norm $H^s$ on the diffeomorphisms group of the circle is geodesically complete, provided $s>3/2$.

17 pages

References in corpus (2)

• The Lagrangian Radon Transform and the Weil representation
• Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

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