Triply periodic minimal and constant mean curvature surfaces, paper for submission to the Royal Society: kgb1.pdf, kgb2.pdf, kgb3.pdf (5 to 7 MB each).

K. Grosse-Brauckmann: Publications

  • with R. Kusner: Conjugate Plateau constructions for homogeneous 3-manifolds, in progress
  • with M. Saba, M. Thiel, M. D. Turner, S. T. Hyde, M. Gu, D. N. Neshev, K. Mecke, and G. E. Schröder-Turk: Circular Dichroism in Biological Photonic Crystals and Cubic Chiral Nets, Phys. Rev. Lett. 106, 103902 (2011)
  • with N. Korevaar, J. Ratzkin, R. Kusner, J. Sullivan:Coplanar k-unduloids are nondegenerate, International Mathematics Research Notices, Vol. 2009, No. 18, 3391-3416, accessible under doi: 10.1093/imrn/rnp058, also arXiv 2008
  • with R. Kusner, J. Sullivan: Coplanar constant mean curvature surfaces, Comm. Anal. Geom. 5,  985--1023, 2007, also arXiv 2005/2007
  • with Yong He: Bifurcations of the nodoids, Oberwolfach Reports 4, 2007, 1327-1228 (a full publication is planned)
  • Cousins of constant mean curvature surfaces, Clay mathematics proceedings 2, 747--767, 2005 (link to entire book, 26 MB)
  • with R. Kusner, J. Sullivan: Triunduloids: Embedded constant mean curvature surfaces with three ends and genus zero, J. reine angew. Maht. 564, 2003, 35-61, also arXiv 2001/03
  • with R. Kusner, J. Sullivan: Constant mean curvature surfaces with three ends, Proc. Natl. Acad. Sci. USA 97, 2000, 14067-14068
  • with R. Kusner: Embedded constant mean curvature surfaces with special symmetry, Man. Math.99, 135-150, 1999
  • with R. Kusner, J. Sullivan: Constant mean curvature surfaces with cylindrical ends, pp.107--116 in: Mathematical Visualization
    (H.-C. Hege, K. Polthier, eds.), Springer 1998.
  • Complete embedded constant mean curvature surfaces (ps.gz, 10 MB), Habilitationsschrift, Bonn 1998
  • On gyroid interfaces, J. Colloid and Interface Science 187, 1997, 418-428
  • with K. Polthier: Constant mean curvature surfaces derived from Delaunay's and Wente's examples, in: Visualization and Mathematics (H.-C. Hege, K. Polthier, eds.), Springer 1997.
  • Constant mean curvature gyroids, Exp. Math. 6, 1997, 21-38
  • with K. Polthier: Compact constant mean curvature surfaces with low genus, Exp. Math. 6, 1-20, 1997
  • with M. Wohlgemuth: The gyroid is embedded and has constant mean curvature companions, Calc. Var. 4, 1996, 499-523
  • Stable constant mean curvature surfaces minimize area, Pac. J. Math. 175,  527-534, 1996
  • with K. Polthier: Numerical examples of compact constant mean curvature surfaces, In: Elliptic and Parabolic Methods in Geometry (B. Chow, R. Gulliver, S. Levy, J. Sullivan, eds.), 23--46, A K Peters, Wellesley (MA), 1996
  • New surfaces of constant mean curvature, Math. Z. 214, 527-565, 1992
  • Interior and boundary monotonicity formulas for stationary harmonic maps, Man. Math 77, 89-95, 1992
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