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
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Loop group methods for the non-abelian Hodge correspondence on a 4-punctured sphere
with Lynn Heller and Martin Traizet
Preprint: arxiv: 2205.12106
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Fuchsian DPW potentials for Lawson surfaces
with Lynn Heller
Preprint: arxiv: 2202.05184
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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
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Complete families of embedded high genus CMC surfaces in the 3-sphere
with Lynn Heller and Martin Traizet
Preprint: arxiv: 2108.10214
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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
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Exploring the Space of Compact Symmetric CMC Surfaces.
With Sebastian Heller and Nicholas Schmitt
Preprint: arXiv:1503.07838
Accepted and published
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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
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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
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Candidates for non-rectangular constrained Willmore minimizers
With Cheikh Birahim Ndiaye
J. Geom. Phys., volume 165, paper no. 104221, 2021
Preprint: arXiv:1902.09572
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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
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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
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Generalized Whitham flow and its applications
Minimal surfaces: Integrable Systems and Visualization, Springer Proceedings in Mathematics and Statistics 348, pp 131--146, 2021
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Higher solutions of Hitchin's self-duality equations
With Sebastian Heller
J. Int. Syst., volume 5, no.1, xyaa006, 2020
Preprint: arXiv:1801.02402.
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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
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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
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Dirac Tori
Differ. Geom. Appl., vol. 54, Part A, pp. 122-128, 2017
Preprint: arXiv:1401.7449
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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
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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
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Constrained Willmore and CMC tori in the 3-sphere
Differ. Geom. Appl., vol. 40, pp 232-242, 2015.
Preprint: arXiv:1212.2068
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Equivariant Constrained Willmore Tori in the 3-Sphere
Math. Z., vol. 278, no. 3, pp 955-977, 2014
Preprint: arXiv:1211.4137
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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
Constrained Willmore Hopf tori
Oberwolfach Reports, vol. 10, no. 2., 2013
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Equivariant Constrained Willmore Tori in S^3.
PhD Thesis, Eberhard Karls University Tübingen, 2012.