Lynn Heller

I am a research fellow (research professor) at
Beijing Institute of Mathematics Sciences and Applications (BIMSA)
Huairou, Beijing

Email: lynn@bimsa.cn

Research


My research lies in the field of Global Surface Geometry. I am investigating constrained Willmore tori, i.e., critical points of the Willmore energy with prescribed conformal class, and CMC surfaces (of higher genus) using the Integrable Systems approach, where moduli spaces of flat connections naturally appear.
I am particularly interested in the interplay between Algebraic Geometric data of the surfaces coming from Integrable Systems (e.g., Higgs bundles, spectral curves) and their analytic properties (e.g., non degeneracy and stability) studied in Geometric Analysis.

Experimental minimizers of Willmore energy with prescribed conformal class. Images by Nick Schmitt .

Publications


Preprints


  1. Loop group methods for the non-abelian Hodge correspondence on a 4-punctured sphere

    with Lynn Heller and Martin Traizet
    Preprint: arxiv: 2205.12106

  2. Fuchsian DPW potentials for Lawson surfaces

    with Lynn Heller
    Preprint: arxiv: 2202.05184

  3. On the existence of holomorphic curves in compact quotients of SL(2,C)

    with Indranil Biswas, Sorin Dumitrescu and Lynn Heller
    Preprint: arxiv: 2112.03131

  4. Complete families of embedded high genus CMC surfaces in the 3-sphere

    with Lynn Heller and Martin Traizet
    Preprint: arxiv: 2108.10214

  5. Holomorphic sl(2,C)-systems with Fuchsian monodromy (with an appendix by Takuro Mochizuki)

    with Indranil Biswas, Sorin Dumitrescu and Lynn Heller
    Preprint: arxiv: 2104.04818

  6. Exploring the Space of Compact Symmetric CMC Surfaces.

    With Sebastian Heller and Nicholas Schmitt
    Preprint: arXiv:1503.07838


Accepted and published


  1. Area estimates for high genus Lawson surfaces via DPW

    with Lynn Heller and Martin Traizet
    accepted for publication in Journal of Differential Geometry
    Preprint: arxiv: 1907.07139

  2. First explicit constrained Willmore minimizers of non-rectangular conformal class.

    Adv. Math., volume 386, paper no. 107804, 2021 With Cheikh Birahim Ndiaye
    Preprint: arXiv:1710.00533

  3. Candidates for non-rectangular constrained Willmore minimizers

    With Cheikh Birahim Ndiaye
    J. Geom. Phys., volume 165, paper no. 104221, 2021
    Preprint: arXiv:1902.09572

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

    With Sebastian Heller and Cheikh Birahim Ndiaye
    Differ. Geom. Phys., volume 79, paper no. 101805, 2021
    Preprint: arXiv:1903.11830

  5. Isothermic constrained Willmore tori in the 3-space

    With Sebastian Heller and Cheikh Birahim Ndiaye
    Ann. Glob. Anal. Geom., volume 60, pp 231--251,2021
    Preprint: arXiv:1903.11823

  6. Generalized Whitham flow and its applications

    Minimal surfaces: Integrable Systems and Visualization, Springer Proceedings in Mathematics and Statistics 348, pp 131--146, 2021

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

    With Sebastian Heller
    J. Int. Syst., volume 5, no.1, xyaa006, 2020
    Preprint: arXiv:1801.02402.

  8. Navigating the Space of Symmetric CMC Surfaces

    With Sebastian Heller and Nicholas Schmitt
    J. Differ. Geom., volume 110, no. 3, pp413--455, 2018
    Preprint: arXiv:1501.01929

  9. Towards a constrained Willmore conjecture

    With Franz Pedit
    Willmore energy and Willmore conjecture, pp 119--138, Monogr. Res. Notes Math., CRC Press, Boca Raton, FL, 2018
    Preprint: arXiv:1705.03217

  10. Dirac Tori

    Differ. Geom. Appl., vol. 54, Part A, pp. 122-128, 2017
    Preprint: arXiv:1401.7449

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

    With Sebastian Heller and Nicholas Schmitt
    J. Geom. Phys., vol 98, pp 201-213, 2015
    Preprint: arXiv:1503.00969

  12. Abelianization of Fuchsian systems on a 4-punctured sphere and applications

    With Sebastian Heller
    J. Symplect. Geom., vol. 14, no. 4, pp. 1059-1088, 2016
    Preprint: arXiv:1404.7707

  13. Constrained Willmore and CMC tori in the 3-sphere

    Differ. Geom. Appl., vol. 40, pp 232-242, 2015.
    Preprint: arXiv:1212.2068

  14. Equivariant Constrained Willmore Tori in the 3-Sphere

    Math. Z., vol. 278, no. 3, pp 955-977, 2014
    Preprint: arXiv:1211.4137

  15. Constrained Willmore Tori and Elastic Curves in 2-Dimensional Space Forms.

    Comm. Anal. Geom., vol. 22, no. 2, pp 343-369, 2014
    Preprint: arXiv:1303.1445

  16. Constrained Willmore Hopf tori


    Oberwolfach Reports, vol. 10, no. 2., 2013

  17. Equivariant Constrained Willmore Tori in S^3.

    PhD Thesis, Eberhard Karls University Tübingen, 2012.