Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Annals of Global Analysis and Geometry

Volumn 44, Issue 4, 2013, Pages 361-368

  Bauer, Martin ^a   Bruveris, Martins ^b   Michor, Peter W ^a  

^a UNIVERSITY OF VIENNA   (Austria)

^b EPFL   (Switzerland)

Author keywords

Diffeomorphism group; Geodesic distance; Sobolev metrics of non integral order

Indexed keywords

EID: 84888287666     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10455-013-9370-4     Document Type: Article

References (13)

1. Bauer, M., Bruveris, M., Harms, P., Michor, P. W.: Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. Ann. Global Anal. Geom. (2012). doi: 10. 1007/s10455-012-9353-x.
2. Bauer, M., Bruveris, M., Harms, P., Michor, P. W.: Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation. Ann. Global Anal. Geom. 41(4), 461-472 (2012).
3. Eichhorn, J.: Global Analysis on Open Manifolds. Nova Science Publishers Inc., New York (2007).
4. Eichhorn, J.: The boundedness of connection coefficients and their derivatives. Math. Nachr. 152, 145-158 (1991).
5. Greene, R. E.: Complete metrics of bounded curvature on noncompact manifolds. Arch. Math. (Basel) 31(1), 89-95 (1978/1979).
6. p-theory of elliptic differential operators on manifolds of bounded geometry. Acta Appl. Math. 23(3), 223-260 (1991).
7. Mather, J. N.: Commutators of diffeomorphisms. Comment. Math. Helv. 49, 512-528 (1974).
8. n (2012, in preparation).
9. Olver, F. W. J., Lozier, D. W., Boisvert, R. F., Clark, C. W. (eds.): NIST Handbook of Mathematical Functions. U. S. Department of Commerce National Institute of Standards and Technology, Washington, DC (2010).
10. Shubin, M. A.: Spectral theory of elliptic operators on noncompact manifolds. Astérisque 207(5), 35-108 (1992) [Méthodes semi-classiques, Vol. 1 (Nantes, 1991)].
11. Stein, E. M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. N. J. Princeton Mathematical Series, No. 32. Princeton University Press, Princeton (1971).
12. Thurston, W.: Foliations and groups of diffeomorphisms. Bull. Amer. Math. Soc. 80, 304-307 (1974).
13. Triebel, H.: Theory of Function Spaces, II. Volume 84 of Monographs in Mathematics. Birkhäuser Verlag, Basel (1992).