Publications

Lecture Notes

  • Riemannian geometry on manifolds of maps. Notes for a short course held at the summer school Mathematics of Shapes at the IMS in Singapore in July 2016.
    Notes

Preprints

  1. M. Bauer, M. Bruveris, B. Kolev. Fractional Sobolev metrics on spaces of plane curves, 2017.
    arXiv:1703.03323
  2. M. Bauer, M. Bruveris, P. Harms, P. W. Michor. Soliton solution for the elastic metric on spaces of curves, 2017.
    arXiv:1702.04344
  3. M. Bruveris, P. W. Michor. Geometry of the Fisher-Rao metric on the space of smooth densities on a compact manifold, 2016.
    arXiv:1607.04550
  4. M. Bruveris, P. W. Michor, A. Parusiński, A. Rainer. Moser's theorem on manifolds with corners, 2016.
    arXiv:1604.07787

Peer-Reviewed Articles

  1. M. Bruveris, F.-X. Vialard. On completeness of groups of diffeomorphisms. Accepted for publication in J. Eur. Math. Soc., 2017.
    arXiv:1403:2089
  2. M. Bruveris. Regularity of maps between Sobolev spaces, Ann. Glob. Anal. Geom., pp 1–14, 2017. Published first online.
    arXiv:1602.06558
  3. M. Bauer, M. Bruveris, P. Harms, J. Møller-Andersen. A numerical framework for Sobolev metrics on the space of curves. SIAM J. Imaging Sci., 10(1), 47–73, 2017.
    arXiv:1603.03480
  4. M. Bruveris. Optimal reparametrizations in the square root velocity framework. SIAM J. Math. Anal., 2016., 48(6), 4335–4354, 2016.
    arXiv:1507.02728
  5. M. Bauer, M. Bruveris, P. W. Michor. Uniqueness of the Fisher-Rao metric on the space of smooth densities. B. Lond. Math. Soc. , 48(3), 499-506, 2016.
    doi:10.1112/blms/bdw020, arXiv:1411.5577
  6. M. Bauer, M. Bruveris, P. W. Michor Why use Sobolev metrics on the space of curves. Riemannian Computing in Computer Vision . Editors P. Turaga and A. Srivastava. 223-255, 2016.
    doi:10.1007/978-3-319-22957-7_11, arXiv:1502.03229
  7. M. Bauer, M. Bruveris, P. Harms, J. Møller-Andersen Second order elastic metrics on the shape space of curves. 1st Workshp on Differential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories, 2015.
    doi:10.5244/C.29.DIFFCV.9, arXiv:1507.08816
  8. M. Bauer, M. Bruveris, P. Harms, J. Møller-Andersen Curve matching with applications in medical imaging. 5th MICCAI workshop on Mathematical Foundations of Computational Anatomy, 2015.
    arXiv:1506.08840
  9. M. Bruveris, D. D. Holm. Geometry of image registration: the diffeomorphism group and momentum maps. Geometry, Mechanics, and Dynamics. Fields Insitute Communications Volume 73, 19-56, 2015.
    doi:10.1007/978-1-4939-2441-7_2, arXiv:1306.6854
  10. M. Bruveris. Completeness properties of Sobolev metrics on the space of curves. J. Geom. Mech, 7(2), 125-150, 2015.
    doi:10.3934/jgm.2015.7.125, arXiv:1407.0601
  11. M. Bruveris, P. W. Michor, D. Mumford. Geodesic completeness for Sobolev metrics on the space of immersed plane curves. Forum Math. Sigma, 2, e19, 38 pages, 2014.
    doi:10.1017/fms.2014.19, arXiv:1312:4995
  12. M. Bauer, M. Bruveris, S. Marsland and P. W. Michor. Constructing reparametrization invariant metrics on spaces of plane curves. Differ. Geom. Appl., 34C, 139-165, 2014.
    doi:10.1016/j.difgeo.2014.04.008, arXiv:1207:5965
  13. M. Bauer, M. Bruveris, P. W. Michor. \(R\)-transforms for \(H^2\)-metrics on spaces of plane curves. Geom. Imaging Comput., 1(1), 1-56, 2014.
    doi:10.4310/GIC.2014.v1.n1.a1, arXiv:1311.3526
  14. M. Bauer, M. Bruveris, P. W. Michor. The homogeneous Sobolev metric of order one on diffeomorphism groups on the real line. J. Nonlinear Sci, 24(5), 769-808, 2014.
    doi:10.1007/s00332-014-9204-y, arXiv:1209.2836
  15. M. Bauer, M. Bruveris, P. W. Michor. Overview of the geometries of shape spaces and diffeomorphism groups. J. Math. Imaging Vis., 50(1-2), 60-97, 2014.
    doi:10.1007/s10851-013-0490-z, arXiv:1305.1150
  16. M. Bauer, M. Bruveris, P. W. Michor. Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II. Ann. Glob. Anal. Geom., 44(4), 361-368, 2013.
    doi:10.1007/s10455-013-9370-4, arXiv:1211.7254
  17. M. Bauer, M. Bruveris, P. Harms and P. W. Michor. Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. Ann. Glob. Anal. Geom., 44(1), 5-21, 2013.
    doi:10.1007/s10455-012-9353-x, arXiv:1105.0327
  18. M. Bruveris, L. Risser and F.-X. Vialard. Mixture of kernels and iterated semi-direct product of diffeomorphism groups. Multiscale Model. Simul., 10(4), 1344-1368, 2012.
    doi:10.1137/110846324, arXiv:1108.2472
  19. M. Bruveris. The energy functional on the Virasoro-Bott group with the \(L^2\)-metric has no local minima. Ann. Glob. Anal. Geom., 43(4), 385-395, 2012.
    10.1007/s10455-012-9350-0, arXiv:1106.4326
  20. M. Bauer, M. Bruveris, P. Harms and P. W. Michor. Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation. Ann. Glob. Anal. Geom., 41(4), 461-472, 2012.
    doi:10.1007/s10455-011-9294-9, arXiv:1102.0236
  21. M. Bauer, M. Bruveris. A new Riemannian setting for surface registration. 3rd MICCAI workshop on Mathematical Foundations of Computational Anatomy, 2011.
    hal:inria-00624210, arXiv:1106.0620
  22. M. Bruveris, D. Ellis, F. Gay-Balmaz and D. D. Holm. Un-reduction. J. Geom. Mech, 3(4), 363-387, 2011.
    doi:10.3934/jgm.2011.3.363, arXiv:1012.0076
  23. M. Bruveris, F. Gay-Balmaz., D. D. Holm and T. S. Ratiu. The momentum map representation of images. J. Nonlinear Sci, 21(1), 115-150, 2011.
    doi:10.1007/s00332-010-9079-5, arXiv:0912.2990

Other

  • M. Bruveris. How to define Sobolev metrics? Proceedings of Math on the Rocks – Shape Analysis Workshop in Grundsund, pp. 13-16, 2015.
    doi:10.5281/zenodo.33558
  • M. Bauer, M. Bruvreis (eds.). Proceedings of Math in the Cabin – Shape Analysis Workshop in Bad Gastein, 2014.
    hal:01076953v1

Theses