Publications and Preprints - David Brander


Preprints

  1. Families of spherical surfaces and harmonic maps.
    (With F. Tari).
  2. Monge surfaces and planar geodesic foliations.
    (With J. Gravesen).
  3. Bézier curves that are close to elastica.
    (With J.A. Bærentzen, A. Fisker and J. Gravesen).

Journal Articles
[Preprints can be found at http://arxiv.org/find]

  1. On the Björling problem for Willmore surfaces.
    (With Peng Wang.)
    J. Differential Geom. (To appear).             Some Images.
  2. Remarks on the boundary curve of a constant mean curvature topological disc.
    (With Rafael Lopez)
    Complex Var. Elliptic Equ. (2017) DOI: 10.1080/17476933.2016.1260558
  3. Pseudospherical surfaces with singularities.
    Ann. Mat. Pura Appl. (2016), DOI: 10.1007/s10231-016-0601-8             Related software.      
  4. Spherical Surfaces.
    Exp. Math., 25:3 (2016), 257-272, DOI: 10.1080/10586458.2015.1077359.
  5. Approximation by planar elastic curves.
    (With Jens Gravesen and Toke Nørbjerg.)
    Adv. Comput. Math. DOI: 10.1007/s10444-016-9474-z
  6. Constant Gaussian curvature surfaces in the 3-sphere via loop groups.
    (With J Inoguchi and S-P Kobayashi.)
    Pacific J. Math. Vol. 269 (2014), No. 2, 281–303.
  7. Deformations of constant mean curvature surfaces preserving symmetries and the Hopf differential.
    (With Josef F. Dorfmeister.)
    Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XIV (2015), 645-675.
  8. Timelike constant mean curvature surfaces with singularities.
    (With M Svensson.)
    J. Geom. Anal. 24 (2014), no. 3, 1641–1672.
  9. The geometric Cauchy problem for surfaces with Lorentzian harmonic Gauss maps.
    (With M Svensson.)
    J. Differential Geom. 93, (2013), 37-66.             Related software.
  10. Singularities of spacelike constant mean curvature surfaces in Lorentz-Minkowski space.
    Math. Proc. Cambridge Philos. Soc. 150, (2011), 527-556.   
  11. The Björling problem for non-minimal constant mean curvature surfaces.
    (With Josef F. Dorfmeister.)
    Comm. Anal. Geom. 18 (2010) 171-194.
  12. Loop group decompositions in almost split real forms and applications to soliton theory and geometry.
    J. Geom. Phys. 58 (2008) 1792-1800.
  13. Holomorphic representation of constant mean curvature surfaces in Minkowski space: consequences of non-compactness in loop group methods.
    (With W Rossman and N Schmitt.)
    Adv. Math. 223 (2010) 949-986. doi:10.1016/j.aim.2009.09.006.
  14. Results related to generalizations of Hilbert's non-immersibility theorem for the hyperbolic plane.
    Electron. Res. Announc. Math. Sci. 15 (2008), 8-16.
  15. Grassmann geometries in infinite dimensional homogeneous spaces and an application to reflective submanifolds.
    Int. Math. Res. Not. IMRN 2007: rnm092-38.
  16. A loop group formulation for constant curvature submanifolds of pseudo-Euclidean space.
    (With W Rossman.)
    Taiwanese J. Math. Vol. 12, No. 7, (2008) pp 1739-1749.
  17. Curved flats, pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms.
    Ann. Global Anal. Geom. 32 (2007), 253-275.
  18. Generalized DPW method and an application to isometric immersions of space forms.
    (With Josef F. Dorfmeister.)
    Math. Z. 262 (2009), 143-172.
  19. K-symmetric AKS systems and flat immersions in spheres.
    J. London. Math. Soc. (2) 77 (2008), 299-319.

Conference Proceedings Articles

  1. Surfaces foliated by planar geodesics: a model for curved wood design.
    (With Jens Gravesen.)
    Proceedings of Bridges Waterloo 2017: Mathematics, Music, Art, Architecture, Education, Culture.
  2. Designing for hot-blade cutting: geometric approaches for high-speed manufacturing of doubly-curved architectural surfaces.
    (With A Bærentzen, K Clausen, A Fisker, J Gravesen, M Lund, T Nørbjerg, K Steenstrup and A Søndergaard)
    Proceedings of Advances in Architectural Geometry, Zurich 2016.
  3. Robotic hot-blade cutting.
    (With A. Søndegaard et al.)
    Robotic Fabrication in Architecture, Art and Design 2016, proceedings of RobArch 2016.
  4. Surfaces with Natural Ridges.
    (With Steen Markvorsen.)
    Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture.
  5. Hot blade cuttings for the building industries.
    (With J.A. Bærentzen, A. Evgrafov, J. Gravesen, S. Markvorsen, T. Nørbjerg, P. Nørtoft and K. Steenstrup.)
    In: Proceedings of the KoMSO Challenge Workshop: Math for the Digital Factory (2014), 2016, Springer.
  6. Geometric Cauchy problems for spacelike and timelike CMC surfaces in R^(2,1).
    RIMS Kokyuroku, No. 1775 (2012), 85--93.
  7. Constant mean curvature surfaces in Euclidean and Minkowski 3-spaces.
    J. Geom. Symmetry Phys. 12 (2008) 15-26.
  8. Grassmann geometries and integrable systems.
    RIMS Kokyuroku, No. 1577 (2008), 64--74. arXiv:0804.1830 [math.DG]
  9. An application of a 3-involution loop group to reflective submanifolds.
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 24/2007, 1334--1337.
  10. Finite type isometric immersions of constant curvature submanifolds.
    Integrable systems, geometry and visualization, Kyushu, 2004.

Dissertations

  1. Flat submanifolds of a sphere and integrable systems.
    Australian National University , Ph.D.
  2. Isometric embeddings between space forms.
    University of Pennsylvania , M.Phil.
  3. The Atiyah-Singer Index Formula for Elliptic Operators.
    University of Oxford , M.Sc.

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