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

Boris Kolev (I2M); Joachim Escher (IFAM)

arxiv: 1308.3570 · v2 · pith:XXSSZYAAnew · submitted 2013-08-16 · 🧮 math-ph · math.MP

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

Joachim Escher (IFAM) , Boris Kolev (I2M) This is my paper

classification 🧮 math-ph math.MP

keywords circlediffeomorphismsgroupsobolevcompletecompletenessfractionalgeodesic

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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 $s>3/2$.

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

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