Hi, I'm Glen Wheeler.

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Building 39C, Office 184

Northfields Ave

Wollongong, NSW, Australia

I’m a mathematician at the University of Wollongong (Australia) working at the interface of geometry and analysis, with a particular focus on the dynamics of geometric evolution equations and higher-order flows. My PhD examined fourth-order geometric evolution equations. After that, I held an Alexander von Humboldt Research Fellowship at Otto von Guericke Universität Magdeburg with Prof. Dr. Hans-Christoph Grunau, continuing work on the dynamics of higher-order geometric flows.

I have just become an ARC Future Fellow (2026–2030) (FT250100880), developing new perspectives on the Cartan–Hadamard conjecture and on Yau’s problem about the equivalence of plane curves. I’m very excited to start the fellowship!

I am also a Chief Investigator on an ARC Discovery Project (2025–2027) (DP250101080) using mathematics to model bushfire dynamics. So far, this project has led to [1], [8], [10], and [17], including: a new model; the first existence–uniqueness results for that model; a study of moving fronts; and an analysis of how policy shapes the efficacy of bushfire response.

Previously, I was a Chief Investigator on an ARC Discovery Project (2015–2018) (DP150100375) focused on geometric flows. That grant catalysed much of my work on fourth-order flows—curve and surface diffusion, elastic/Willmore flows—as well as fully nonlinear second-order flows with non-smooth speeds and polyharmonic flows. It launched my research program and laid durable foundations for ongoing collaborations.

My work and teaching have been recognised with the biennial Peter Schwerdtfeger Award and the AustMS Early Career Teaching Excellence Award. I enjoy clear exposition, collaboration, and finding new connections between curvature, PDE, and real-world phenomena.

I have published specifically on the following topics:

1. Curve and surface diffusion

  1. Rybka, P., & Wheeler, G. (2025). A classification of solitons for the surface diffusion flow of entire graphs. Physica D: Nonlinear Phenomena, 134702.
  2. Wheeler, G., & Wheeler, V.-M. (2024). Curve diffusion and straightening flows on parallel lines. Communications in Analysis and Geometry.
  3. Wheeler, G. (2021). Convergence for global curve diffusion flows. Mathematics In Engineering, 4(1), 1.
  4. McCoy, J., Wheeler, G., & Wu, Y. (2019). Evolution of closed curves by length-constrained curve diffusion. Proceedings of the American Mathematical Society, 147(8), 3493–3506.
  5. Edwards, M., Gerhardt-Bourke, A., McCoy, J., Wheeler, G., & Wheeler, V.-M. (2016). The shrinking figure eight and other solitons for the curve diffusion flow. The Mechanics of Ribbons and Möbius Bands, 191–211.
  6. Wheeler, G. (2012). Surface diffusion flow near spheres. Calculus of Variations and Partial Differential Equations, 44(1), 131–151.
  7. Wheeler, G. (2012). On the curve diffusion flow of closed plane curves. Annali Di Matematica Pura Ed Applicata, 1–20.

2. Families of fourth order flows

  1. Simon, M., & Wheeler, G. (2016). Some local estimates and a uniqueness result for the entire biharmonic heat equation. Advances in Calculus of Variations, 9(1), 77–99.
  2. Wheeler, G. (2015). Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary. Proceedings of the American Mathematical Society, 143(4), 1719–1737.
  3. Wheeler, G. (2011). Lifespan theorem for simple constrained surface diffusion flows. Journal of Mathematical Analysis and Applications, 375(2), 685–698.
  4. McCoy, J., Wheeler, G., & Williams, G. (2011). Lifespan theorem for constrained surface diffusion flows. Mathematische Zeitschrift, 269(1), 147–178.
  5. Wheeler, G. (2010). Fourth order geometric evolution equations. Bulletin of the Australian Mathematical Society, 82(3), 523–524.

3. Elastic, Willmore and Helfrich

  1. Andrews, B., & Wheeler, G. (2026). Jellyfish exist. ArXiv Preprint ArXiv:2601.21227.
  2. Miura, T., & Wheeler, G. (2025). Uniqueness and minimality of Euler’s elastica with monotone curvature. Journal of the European Mathematical Society.
  3. Miura, T., & Wheeler, G. (2025). The free elastic flow for closed planar curves. Journal of Functional Analysis, 111030.
  4. Andrews, B., & Wheeler, G. (2025). On the planar free elastic flow with small oscillation of curvature. ArXiv Preprint ArXiv:2509.11129.
  5. Deckelnick, K., Grunau, H.-C., Nürnberg, R., Wheeler, G., & Wheeler, V.-M. (2025). On the basin of attraction for the free boundary free elastic flow. ArXiv Preprint ArXiv:2512.19015.
  6. Bernard, Y., Wheeler, G., & Wheeler, V.-M. (2023). Analysis of the inhomogeneous Willmore equation. Annales De l’Institut Henri Poincaré C, 41(1), 129–158.
  7. Okabe, S., & Wheeler, G. (2023). The p-elastic flow for planar closed curves with constant parametrization. Journal De Mathématiques Pures Et Appliquées, 173, 1–42.
  8. Okabe, S., Pozzi, P., & Wheeler, G. (2020). A gradient flow for the p-elastic energy defined on closed planar curves. Mathematische Annalen, 378(1), 777–828.
  9. McCoy, J., & Wheeler, G. (2016). Finite time singularities for the locally constrained Willmore flow of surfaces. Communications in Analysis and Geometry, 24(4), 843–886.
  10. Wheeler, G. (2015). Global analysis of the generalised Helfrich flow of closed curves immersed in \mathbbR^n. Transactions of the American Mathematical Society, 367(4), 2263–2300.
  11. McCoy, J., & Wheeler, G. (2013). A classification theorem for Helfrich surfaces. Mathematische Annalen, 357, 1485–1508.
  12. Dall’Acqua, A., Deckelnick, K., & Wheeler, G. (2013). Unstable Willmore surfaces of revolution subject to natural boundary conditions. Calculus of Variations and Partial Differential Equations, 48, 293–313.

4. Fire, thin films, wound healing and biomembranes

  1. Dipierro, S., Valdinoci, E., Wheeler, G., & Wheeler, V.-M. (2026). Existence theory for a bushfire equation. Journal of Differential Equations, 452, 113821. https://doi.org/https://doi.org/10.1016/j.jde.2025.113821
  2. Morandotti, M., Rybka, P., & Wheeler, G. (2026). Stabilization of solutions to a model of Langmuir-Blodgett films. ArXiv Preprint ArXiv:2603.16787.
  3. Dipierro, S., Valdinoci, E., Wheeler, G., & Wheeler, V.-M. (2025). Bushfires and Balance: Proactive versus Reactive Policies in Prescribed Burning. Math. Model. Nat. Phenom., 20, 24. https://doi.org/10.1051/mmnp/2025023
  4. Dipierro, S., Valdinoci, E., Wheeler, G., & Wheeler, V.-M. (2025). Self-sustaining traveling fronts for a model related to bushfires. ArXiv Preprint ArXiv:2504.21365.
  5. He, S., Whale, B., Wheeler, G., & Wheeler, V.-M. (2025). A curvature flow approach to dorsal closure modelling. ArXiv Preprint ArXiv:2507.12088.
  6. Dipierro, S., Valdinoci, E., Wheeler, G., & Wheeler, V.-M. (2024). A simple but effective bushfire model: analysis and real-time simulations. SIAM Journal on Applied Mathematics, 84(4), 1504–1514.
  7. Rybka, P., & Wheeler, G. (2023). Convergence of Solutions to a Convective Cahn–Hilliard-Type Equation of the Sixth Order in Case of Small Deposition Rates. SIAM Journal on Mathematical Analysis, 55(5), 5823–5861.
  8. He, S., Wheeler, G., & Wheeler, V.-M. (2019). On a curvature flow model for embryonic epidermal wound healing. Nonlinear Analysis, 189, 111581.
  9. Bernard, Y., Wheeler, G., & Wheeler, V.-M. (2018). Rigidity and stability of spheres in the Helfrich model. Interfaces and Free Boundaries, 19(4), 495–523.
  10. Wheeler, V. M., Wheeler, G. E., McCoy, J. A., & Sharples, J. J. (2015). Modelling dynamic bushfire spread: perspectives from the theory of curvature flow. MODSIM2015, 21st International Congress on Modelling and Simulation, 319–325.
  11. Wheeler, V.-M., McCoy, J. A., Wheeler, G., & Sharples, J. J. (2013). Curvature flows and barriers in fire front modelling. MODSIM.
  12. Sharples, J. J., Towers, I. N., Wheeler, G., Wheeler, V.-M., & McCoy, J. A. (2013). Modelling fire line merging using plane curature flow. MODSIM.

5. Chen’s conjecture and flow

  1. Cooper, M. K., Wheeler, G., & Wheeler, V.-M. (2023). Theory and numerics for Chen’s flow of curves. Journal of Differential Equations, 362, 1–51.
  2. Bernard, Y., Wheeler, G., & Wheeler, V.-M. (2019). Concentration-Compactness and Finite-Time Singularities for Chen’s Flow. J. Math. Sci. Univ. Tokyo, 26, 55–139.
  3. Wheeler, G. (2013). Chen’s conjecture and \varepsilon-superbiharmonic submanifolds of Riemannian manifolds. International Journal of Mathematics, 24(04), 1350028.

6. Flows of arbitrary order

  1. McCoy, J. A., Schrader, P., & Wheeler, G. (2023). Representation formulae for higher order curvature flows. Journal of Differential Equations, 344, 1–43.
  2. McCoy, J., Wheeler, G., & Wu, Y. (2022). High order curvature flows of plane curves with generalised Neumann boundary conditions. Advances in Calculus of Variations, 15(3), 497–513.
  3. Parkins, S., & Wheeler, G. (2019). The anisotropic polyharmonic curve flow for closed plane curves. Calculus of Variations and Partial Differential Equations, 58(2), 70.
  4. Parkins, S., & Wheeler, G. (2016). The polyharmonic heat flow of closed plane curves. Journal of Mathematical Analysis and Applications, 439(2), 608–633.

Sixth-order flows

  1. McCoy, J., Wheeler, G., & Wu, Y. (2020). A sixth order flow of plane curves with boundary conditions. Tohoku Mathematical Journal, 72(3), 379–393.
  2. Droniou, J., Ilyas, M., Lamichhane, B. P., & Wheeler, G. E. (2019). A mixed finite element method for a sixth-order elliptic problem. IMA Journal of Numerical Analysis, 39(1), 374–397.
  3. McCoy, J., Wheeler, G., & Wu, Y. (2019). A sixth order curvature flow of plane curves with boundary conditions. 2017 MATRIX Annals, 213–221.
  4. McCoy, J., Parkins, S., & Wheeler, G. (2017). The geometric triharmonic heat flow of immersed surfaces near spheres. Nonlinear Analysis, 161, 44–86.

7. Second-order flows

  1. Cuthbertson, S., Wheeler, G., & Wheeler, V.-M. (2025). Curve shortening flow with an ambient force field. Calculus of Variations and Partial Differential Equations, 64(5), 154.
  2. Cuthbertson, S., Wheeler, G., & Wheeler, V. (2024). A curvature flow that deforms curves to an embedded target. ArXiv Preprint ArXiv:2411.18951.
  3. Kwong, K.-K., Wei, Y., Wheeler, G., & Wheeler, V.-M. (2022). On an inverse curvature flow in two-dimensional space forms. Mathematische Annalen, 384(1), 1–24.
  4. Wheeler, G., & Wheeler, V.-M. (2020). Mean curvature flow with free boundary–Type 2 singularities. Mathematische Nachrichten, 293(4), 794–813.
  5. Wheeler, G., & Wheeler, V.-M. (2019). Minimal hypersurfaces in the ball with free boundary. Differential Geometry and Its Applications, 62, 120–127.
  6. Wheeler, G., & Wheeler, V.-M. (2017). Mean curvature flow with free boundary outside a hypersphere. Transactions of the American Mathematical Society, 369(12), 8319–8342.
  7. Andrews, B., Holder, A., McCoy, J., Wheeler, G., Wheeler, V.-M., & Williams, G. (2017). Curvature contraction of convex hypersurfaces by nonsmooth speeds. Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal), 2017(727), 169–190.
  8. Drugan, G., Lee, H., & Wheeler, G. (2016). Solitons for the inverse mean curvature flow. Pacific Journal of Mathematics, 284(2), 309–326.

8. Ideal flow

  1. Mccoy, J. A., Wheeler, G. E., & Wu, Y. (2022). A Length-Constrained Ideal Curve Flow. The Quarterly Journal of Mathematics, 73(2), 685–699.
  2. Andrews, B., McCoy, J., Wheeler, G., & Wheeler, V.-M. (2020). Closed ideal planar curves. Geometry & Topology, 24(2), 1019–1049.
  3. McCoy, J., & Wheeler, G. (2020). A rigidity theorem for ideal surfaces with flat boundary. Annals of Global Analysis and Geometry, 57(1), 1–13.

9. Entropy flow

  1. O’Donnell, L., Wheeler, G., & Wheeler, V.-M. (2024). The gradient flow for entropy on closed planar curves. Archive for Rational Mechanics and Analysis, 248(4), 68.

10. Sobolev gradient flows

  1. Okabe, S., Schrader, P., Wheeler, G., & Wheeler, V.-M. (2025). A Sobolev gradient flow for the area-normalised Dirichlet energy of H^1 maps. Advances in Calculus of Variations.
  2. Schrader, P., Wheeler, G., & Wheeler, V.-M. (2023). On the H^1(ds^γ)-Gradient Flow for the Length Functional. The Journal of Geometric Analysis, 33(9), 297.

11. Invariant flows in fundamental geometries

  1. Andrews, B., & Wheeler, G. (2025). The curve-lengthening flow in inversive geometry. ArXiv Preprint ArXiv:2502.17896.

Links to my ORCiD, Google Scholar, and other external sites are in the header and footer of this page. If you wish to get in touch, please feel free to use my email.

Geometric Analysis Zulip Server. If you are interested in joining our Zulip server, please email geometricanalysiszulip@gmail.com. The YouTube channel for our seminar series aimed at PhD students and young researchers is also linked below. The homepage of the seminar is here.

Editorial work. I am on the editorial board for Journal of Evolution Equations (link) 2025-present, the Bulletin of the Australian Mathematical Society (link) 2025-present, and Transactions in Pure and Applied Mathematics (link) 2026-present. I have served as guest editor for the MATRIX Annals (link) for special issues attached to conferences held at MATRIX that I have organised.

Governance. I am currently the Associate Head of School (Mathematics and Statistics) at the University of Wollongong, within the School of Mathematics and Physics. I serve on the Executive of the Australian Association of Alexander von Humboldt fellows as the NSW representative, and have done so since 2021. (If you would like some advice regarding applications for Humboldt Fellowships, please let me know!) I am also recently elected to the Council of the Australian Mathematical Society (from 2025). Locally, I have long held the chair of the School Education Committee (2016-2021, 2024-2025), leading curriculum reform and shaping service relationships. I have also served in a number of other minor governance roles, for instance as academic integrity officer and academic program director.

Phd Supervision. I have supervised Scott Parkins (2017), Lachlan Macdonald (2019), Shuhui He (2019) ,Yuhan Wu (2021), Sam Cuthbertson (2025), and Lachlann O’Donnell (2025) to PhD completion. I am currently supervising Ben Whale, Vindula Kumaranayake, and Dinh Dat.