Lynn Heller

activity

20122026

most citedNavigating the Space of Symmetric CMC Surfaces

11 citations · 31 across the 20 of their papers we have counts for

collaborators

27 papers

math.DG2026

Non-algebraicity of the Lawson surfaces $ξ_{k, l}$

Lynn Heller, Sebastian Heller

We prove that every Lawson surface $ξ_{k, l} \subset S^{3}$ of genus $k l > 1$ is non-algebraic: any real polynomial vanishing on $ξ_{k, l}$ vanishes identically on $S^{3}$ . T…

math.DG2026

The Enclosed Volume for Periodic Constant Mean Curvature Surfaces

Lynn Heller, Sebastian Heller, Martin Traizet

We establish a general formula for the enclosed volume of constant mean curvature (CMC) surfaces in Euclidean three space with translational periods forming a lattice. The formula…

math.DG2025

Semiclassical Limits of Strongly Parabolic Higgs Bundles and Hyperpolygon Spaces

Lynn Heller, Sebastian Heller, Claudio Meneses

We investigate the Hitchin hyperkähler metric on the moduli space of strongly parabolic $\mathfrak{sl}(2,\C)$-Higgs bundles on the $n$ -punctured Riemann sphere and its degeneration…

math.DG2025

Application of Chern-Simons gauge theory to the enclosed volume of constant mean curvature surfaces in the 3-sphere

Lynn Heller, Sebastian Heller, Martin Traizet

Building on Hitchin's work of the Wess-Zumino-Witten term for harmonic maps into Lie groups, we derive a formula for the enclosed volume of a compact CMC surface $f$ in $\mathbb S^…

math.DG2024

Minimal surfaces and alternating multiple zetas

Steven Charlton, Lynn Heller, Sebastian Heller +1

In this paper we show for every sufficiently large integer $g$ the existence of a complete family of closed and embedded constant mean curvature (CMC) surfaces deforming the Lawson…

math.DG2023

On the monodromy of holomorphic differential systems

Indranil Biswas, Sorin Dumitrescu, Lynn Heller +2

First we survey and explain the strategy of some recent results that construct holomorphic $sl (2, C)$ -differential systems over some Riemann surfaces $Σ_{g}$ of genus…

math.DG2023

Holomorphic Higgs bundles over the Teichmüller space

Indranil Biswas, Lynn Heller, Sebastian Heller

We study which representations $ρ$ of the fundamental group of a compact oriented surface $X$ admit Higgs data that depend holomorphically on the Riemann surface $Σ = (X, J)$ …

math.DG2022

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

Lynn Heller, Sebastian Heller, Martin Traizet

The non-abelian Hodge correspondence is a real analytic map between the moduli space of stable Higgs bundles and the deRham moduli space of irreducible flat connections mediated by…

math.DG2022

Fuchsian DPW potentials for Lawson surfaces

Lynn Heller, Sebastian Heller

The Lawson surfaces $ξ_{1, g}$ of genus $g$ are constructed by rotating and reflecting the Plateau solution $f_{t}$ with respect to a particular geodesic $4$ -gon $Γ_{t}$ along its bound…

math.AG2021

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

Indranil Biswas, Sorin Dumitrescu, Lynn Heller +1

We prove the existence of a pair $(Σ, Γ)$ , where $Σ$ is a compact Riemann surface with $genus (Σ) \geq 2$ , and $Γ \subset S L (2, C)$ is a cocompact…

math.DG2021★ 1 cited

Complete families of embedded high genus CMC surfaces in the 3-sphere (with an appendix by Steven Charlton)

Lynn Heller, Sebastian Heller, Martin Traizet

For every $g ≫ 1$ , we show the existence of a complete and smooth family of closed constant mean curvature surfaces $f_{φ}^{g},$ $φ \in [0, \frac{π}{2}],$ in the round $3$ -sphere defo…

math.AG2021

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

Indranil Biswas, Sorin Dumitrescu, Lynn Heller +1

For every integer $g \geq 2$ we show the existence of a compact Riemann surface $Σ$ of genus $g$ such that the rank two trivial holomorphic vector bundle ${\mathcal O}^{\oplus…

math.DG2019★ 1 cited

Area Estimates for High genus Lawson surfaces via DPW

Lynn Heller, Sebastian Heller, Martin Traizet

Starting at a saddle tower surface, we give a new existence proof of the Lawson surfaces $ξ_{m, k}$ of high genus by deforming the corresponding DPW potential. As a byproduct, we ob…

math.DG2019

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

Lynn Heller, Sebastian Heller, Cheikh Birahim Ndiaye

We show that the of 2-lobed Delaunay tori are stable as constrained Willmore surfaces in the 3-sphere.

math.DG2019

Isothermic constrained Willmore tori in 3-space

Lynn Heller, Sebastian Heller, Cheikh Birahim Ndiaye

We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore energy below $8 π$ . In parti…

math.DG2019★ 1 cited

Rectangular constrained Willmore minimizers and the Willmore conjecture

Lynn Heller, Sebastian Heller, Cheikh Birahim Ndiaye

We show that the well-known family of $2$ -lobed Delaunay tori $f^{b}$ in $S^{3},$ parametrized by $b \in R_{\geq 1},$ uniquely minimizes the Willmore energy among al…

math.DG2019

Candidates for non-rectangular constrained Willmore minimizers

Lynn Heller, Cheikh Birahim Ndiaye

For every $b > 1$ fixed, we explicitly construct $1$ -dimensional families of embedded constrained Willmore tori parametrized by their conformal class $(a, b)$ \; with $\; a \sim_…

math.DG2018★ 3 cited

Higher solutions of Hitchin's self-duality equations

Lynn Heller, Sebastian Heller

Solutions of Hitchin's self-duality equations corresponds to special real sections in the Deligne-Hitchin moduli space -- twistor lines. A question posed by Simpson in 1997 asks wh…

math.DG2017

First explicit constrained Willmore minimizers of non-rectangular conformal class

Lynn Heller, Cheikh Birahim Ndiaye

We study immersed tori in $3$ -space minimizing the Willmore energy in their respective conformal class. Within the rectangular conformal classes $(0, b)$ with $b \sim 1$ the…

math.DG2017

Towards a constrained Willmore conjecture

Lynn Heller, Franz Pedit

We give an overview of the constrained Willmore problem and address some conjectures arising from partial results and numerical experiments. Ramifications of these conjectures woul…

math.DG2015★ 2 cited

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

Lynn Heller, Sebastian Heller, Nicholas Schmitt

Constant mean curvature surfaces in $S^{3}$ can be studied via their associated family of flat connections. In the case of tori this approach has led to a deep understanding of the m…

math.DG2015★ 1 cited

Exploring the space of compact symmetric CMC surfaces

Lynn Heller, Sebastian Heller, Nicholas Schmitt

We map out the moduli space of Lawson symmetric constant mean curvature surfaces in the 3-sphere of genus $g > 1$ by flowing numerically from Delaunay tori with even lobe count via t…

math.DG2015★ 11 cited

Navigating the Space of Symmetric CMC Surfaces

Lynn Heller, Sebastian Heller, Nicholas Schmitt

In this paper we introduce a flow on the spectral data for symmetric CMC surfaces in the $3$ -sphere. The flow is designed in such a way that it changes the topology but fixes the i…

math.AG2014

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

Lynn Heller, Sebastian Heller

In this paper we consider special linear Fuchsian systems of rank $2$ on a $4 -$ punctured sphere and the corresponding parabolic structures. Through an explicit abelianization proce…

Non-algebraicity of the Lawson surfaces ξk,l​

The Enclosed Volume for Periodic Constant Mean Curvature Surfaces

Semiclassical Limits of Strongly Parabolic Higgs Bundles and Hyperpolygon Spaces

Application of Chern-Simons gauge theory to the enclosed volume of constant mean curvature surfaces in the 3-sphere

Minimal surfaces and alternating multiple zetas

On the monodromy of holomorphic differential systems

Holomorphic Higgs bundles over the Teichmüller space

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

Fuchsian DPW potentials for Lawson surfaces

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

Complete families of embedded high genus CMC surfaces in the 3-sphere (with an appendix by Steven Charlton)

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

Area Estimates for High genus Lawson surfaces via DPW

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

Isothermic constrained Willmore tori in 3-space

Rectangular constrained Willmore minimizers and the Willmore conjecture

Candidates for non-rectangular constrained Willmore minimizers

Higher solutions of Hitchin's self-duality equations

First explicit constrained Willmore minimizers of non-rectangular conformal class

Towards a constrained Willmore conjecture

The spectral curve theory for (k,l)−symmetric CMC surfaces

Exploring the space of compact symmetric CMC surfaces

Navigating the Space of Symmetric CMC Surfaces

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

Non-algebraicity of the Lawson surfaces $ξ_{k, l}$

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

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

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