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E-mail: heller@mathi.uni-heidelberg.de

Three views of a constant mean curvature surface in the 3-sphere. Images by Nick Schmitt based on the joint paper 'Deformations of symmetric CMC surfaces in the 3-sphere'.

Office Hours

Research

Teaching

Publications

1. Higher solutions of Hitchin's self-duality equations

   with Lynn Heller
   accepted for publication in Journal of Integrable Systems
   Preprint: arxiv: 1801.02402

2. Energy of sections of the Deligne-Hitchin twistor space

   with Florian Beck and Markus Roeser
   published online in Math. Annalen
   Preprint: arxiv: 1903.02497

3. Minimal n-noids in hyperbolic and anti-de Sitter 3-space

   with Alexander I. Bobenko and Nicholas Schmitt
   Proceedings of the Royal Society A, DOI: 10.1098/rspa.2019.0173
   Preprint: arxiv: 1902.07992

4. Real holomorphic sections of the Deligne-Hitchin moduli space

   with I. Biswas and M. Roeser
   Comm. Math. Phys., Volume 366, Issue 3 (2019), pages 1099-1133
   Preprint: arXiv:1802.06587

5. Branes through finite group actions

   with Laura P. Schaposnik
   J. Geom. Phys., Volume 129, July 2018, Pages 279-293
   Preprint: arxiv: 1611.00391

6. Navigating the Space of Symmetric CMC Surfaces

   with Lynn Heller and Nicholas Schmitt
   Journal of Differential Geometry, Vol. 110, No. 3 (2018), pp. 413-455
   Preprint: arxiv: 1501.01929

7. Automorphisms of a rank one Deligne-Hitchin moduli space

   with Indranil Biswas
   SIGMA 13 (2017), 072, 19 pages; online version
   Preprint: arxiv: 1704.04924

8. The asymptotic behavior of the monodromy representations of the associated families of compact CMC surfaces

   Bulletin of the London Mathematical Society 2016; doi: 10.1112/blms/bdw036
   Preprint: arXiv:1505.00747

9. The spectral curve theory for (k,l)-symmetric CMC surfaces

   with Lynn Heller and Nicholas Schmitt
   J. Geom. Phys. 98 (2015), 201-213. http://dx.doi.org/10.1016/j.geomphys.2015.08.010
   Preprint version

10. Abelianization of Fuchsian Systems on a 4-punctured sphere and applications

    with Lynn Heller
    Journal of Symplectic Geometry, Vol. 14, No. 4 (2016), pp. 1059-1088
    Preprint version

11. Conformally flat circle bundles over surfaces

    Diff. Geom. Appl. 40 (2015), 103-110.
    Preprint version

12. Deformations of symmetric CMC surfaces in the 3-sphere

    with Nick Schmitt
    Experimental Mathematics , Volume 24, Issue 1 (2015), pp 65-75.
    Preprint: arxiv: 1305.4107

13. A spectral curve approach to Lawson symmetric CMC surfaces of genus 2

    Math. Annalen, Volume 360, Issue 3 (2014), pp 607-652.
    DOI: 10.1007/s00208-014-1044-4
    Preprint: arxiv: 1209.3200

14. Lawson's genus two minimal surface and meromorphic connections

    Math. Z., Volume 274 (2013), pp 745-760.
    DOI: 10.1007/s00209-012-1094-9
    Preprint version

15. Higher genus minimal surfaces in S^3 and stable bundles.

    J. Reine Angew. Math. (Crelle's Journal), Volume 685 (2013), pp 105-122.
    DOI: 10.1515/crelle-2012-0011
    Preprint version
    Review

16. Higher genus CMC surfaces via integrable systems

    Abresch U, Pedit F, Umehara M.: Progress in Surface Theory. Oberwolfach Rep. Volume 10 (2013), pp 1253-1312.
    DOI: 10.4171/OWR/2013/21
    

17. Conformal fibrations of S3 by circles.

    Harmonic maps and differential geometry, Contemp. Math., Amer. Math. Soc., Providence, RI, Volume 542 (2011), pp 195-202.
    Preprint version
    Review

18. Harmonic morphisms on conformally flat 3-spheres

    Bull. Lond. Math. Soc., Volume 43 (2011), no. 1, 137-150.
    Preprint version

19. Global aspects of integrable surface geometry

    with A. Gerding, F. Pedit and N. Schmitt
    in Systèmes intégrables et théorie des champs quantiques, eds: P. Baird, F. Hélein, J. Kouneiher, F. Pedit, V. Roubtsov, collection Travaux en Cours en Physique-Mathématiques, no 75, Hermann (2009).

Preprints

1. On certain Tannakian categories of integrable connections over Kaehler manifolds

   with Indranil Biswas, Joćo Pedro dos Santos and Sorin Dumitrescu
   
   Preprint: arXiv:2005.02564

2. Branes and moduli spaces of Higgs bundles on smooth projective varieties

   with Indranil Biswas and Laura P. Schaposnik
   
   Preprint: arxiv:2003.06997

3. Irreducible flat SL(2,R)-connections on the trivial holomorphic bundle

   with Indranil Biswas and Sorin Dumitrescu
   
   Preprint: arxiv:2003.06997

4. Willmore spheres in the 3-sphere revisited

   
   Preprint: arxiv:2003.06922

5. Area Estimates for High genus Lawson surfaces via DPW

   with Lynn Heller and Martin Traizet
   
   Preprint: arxiv:1907.07139

6. Real projective structures on Riemann surfaces and new hyper-Kähler manifolds

   Preprint: arXiv:1906.10350

7. Stability properties of 2-lobed Delaunay tori in the 3-sphere

   with Lynn Heller and Cheikh Birahim Ndiaye
   Preprint: arxiv:1903.11830

8. Isothermic constrained Willmore tori in 3-space

   with Lynn Heller and Cheikh Birahim Ndiaye
   Preprint: arxiv: 1903.11823

9. Exploring the space of compact symmetric CMC surfaces

   with Lynn Heller and Nicholas Schmitt
   Preprint: arxiv: 1503.07838

Theses

Integrable systems methods for higher genus CMC surfaces in the 3-sphere

Conformal Submersions of the 3-sphere