Hi, I'm Glen Wheeler.

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Building 39C, Office 184

Northfields Ave

Wollongong, NSW, Australia

I am an ARC Future Fellow and Associate Head (Mathematics and Statistics) in the School of Mathematics and Physics at the University of Wollongong. My research lies at the interface of geometry and analysis, particularly geometric evolution equations, higher-order flows, nonlinear partial differential equations, and Riemannian geometry.

My PhD concerned fourth-order geometric evolution equations. I subsequently held an Alexander von Humboldt Research Fellowship at Otto von Guericke University Magdeburg with Professor Hans-Christoph Grunau, where I continued my work on the dynamics of higher-order geometric flows.

New — 15 July 2026. My paper A simply connected nilpotent Lie group with a closed geodesic has been accepted for publication in the Proceedings of the American Mathematical Society. It constructs a six-dimensional simply connected nilpotent Lie group with a left-invariant Riemannian metric admitting a nonconstant closed geodesic, thereby answering a question of Christoph Böhm and Ramiro Lafuente in the affirmative.

Other papers posted in 2026 concern the generalised ideal flow of closed planar curves, scale-critical curve diffusion flows, Heintze–Karcher and reverse Alexandrov–Fenchel inequalities via focal geometry, the homogeneous Sobolev gradient flow of the length functional, stabilisation in a model of Langmuir–Blodgett films, and the existence of elastic “jellyfish” curves.

I hold an ARC Future Fellowship (2026–2030) (FT250100880) for the project New directions in geometric flows. The fellowship develops new approaches to the Cartan–Hadamard conjecture and to a problem of Yau concerning the equivalence of plane curves.

I am also a Chief Investigator on the ARC Discovery Project Non-local PDE approach to moving fronts and bushfires (2025–2027) (DP250101080). This project has produced a new bushfire model, an existence-and-uniqueness theory for the model, work on self-sustaining travelling fronts, and an analysis of proactive and reactive prescribed-burning policies.

Previously, I was a Chief Investigator on an ARC Discovery Project in geometric flows (2015–2018) (DP150100375). That project supported work on curve and surface diffusion, elastic and Willmore flows, fully nonlinear second-order flows with non-smooth speeds, and polyharmonic flows, and established several continuing collaborations.

My research and teaching have been recognised with the biennial Peter Schwerdtfeger Award and the AustMS Early Career Teaching Excellence Award.

Research areas

My publications are grouped below by research area.

1. Curve and surface diffusion

  1. Miura, T., & Wheeler, G. (2026). Scale-critical curve diffusion flows. ArXiv Preprint ArXiv:2604.01716.
  2. Rybka, P., & Wheeler, G. (2025). A classification of solitons for the surface diffusion flow of entire graphs. Physica D: Nonlinear Phenomena, 477, 134702. https://doi.org/10.1016/j.physd.2025.134702
  3. Wheeler, G., & Wheeler, V.-M. (2024). Curve diffusion and straightening flows on parallel lines. Communications in Analysis and Geometry.
  4. Wheeler, G. (2021). Convergence for global curve diffusion flows. Mathematics In Engineering, 4(1), 1.
  5. 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.
  6. 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.
  7. Wheeler, G. (2012). Surface diffusion flow near spheres. Calculus of Variations and Partial Differential Equations, 44(1), 131–151.
  8. 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. Arbitrary-order curvature flows

  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.

4. Elastic, Willmore, and Helfrich flows

  1. Andrews, B., & Wheeler, G. (2026). Jellyfish exist. ArXiv Preprint ArXiv:2601.21227.
  2. 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.
  3. Miura, T., & Wheeler, G. (2025). The free elastic flow for closed planar curves. Journal of Functional Analysis, 289(7), 111030. https://doi.org/10.1016/j.jfa.2025.111030
  4. Andrews, B., & Wheeler, G. (2025). On the planar free elastic flow with small oscillation of curvature. MATRIX Annals.
  5. Miura, T., & Wheeler, G. (2025). Uniqueness and minimality of Euler’s elastica with monotone curvature. Journal of the European Mathematical Society. https://doi.org/10.4171/JEMS/1708
  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.

5. Fire, thin films, wound healing, and biomembranes

  1. Morandotti, M., Rybka, P., & Wheeler, G. (2026). Stabilization of solutions to a model of Langmuir–Blodgett films. ArXiv Preprint ArXiv:2603.16787.
  2. 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/10.1016/j.jde.2025.113821
  3. He, S., Whale, B., Wheeler, G., & Wheeler, V.-M. (2025). A curvature flow approach to dorsal closure modelling. ArXiv Preprint ArXiv:2507.12088.
  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. 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
  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 curvature flow. MODSIM.

6. Riemannian geometry and geometric inequalities

  1. Wheeler, G. (2026). A simply connected nilpotent Lie group with a closed geodesic. Proceedings of the American Mathematical Society.
  2. Kwong, K.-kun, Parkins, S., & Wheeler, G. (2026). Heintze–Karcher and Reverse Alexandrov–Fenchel Inequalities via Focal Geometry. ArXiv Preprint ArXiv:2603.23946.

7. 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.

8. Polyharmonic and higher-order problems

  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.

9. 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. https://doi.org/10.1007/s00526-025-02983-x
  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.

10. Ideal energy: critical points and its flow

  1. McCoy, J., & Wheeler, G. (2026). On the generalised ideal flow of closed planar curves. ArXiv Preprint ArXiv:2605.09379.
  2. Mccoy, J. A., Wheeler, G. E., & Wu, Y. (2022). A Length-Constrained Ideal Curve Flow. The Quarterly Journal of Mathematics, 73(2), 685–699.
  3. Andrews, B., McCoy, J., Wheeler, G., & Wheeler, V.-M. (2020). Closed ideal planar curves. Geometry & Topology, 24(2), 1019–1049.
  4. McCoy, J., & Wheeler, G. (2020). A rigidity theorem for ideal surfaces with flat boundary. Annals of Global Analysis and Geometry, 57(1), 1–13.

11. 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.

12. Sobolev gradient flows

  1. Schrader, P., Wheeler, G., & Wheeler, V.-M. (2026). Homogeneous Sobolev gradient flow of the length functional. ArXiv Preprint ArXiv:2603.18504.
  2. 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, 18(4), 1085–1104. https://doi.org/10.1515/acv-2024-0081
  3. 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.

13. 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 record, Google Scholar profile, and other external pages are in the header and footer. The best way to contact me is by email.

Seminars and mathematical community

Australian Geometric PDE Seminar and Geometric Analysis Zulip server. I help run a national online seminar series aimed particularly at PhD students and early-career researchers. The seminar homepage and YouTube channel are linked here; to join the associated Zulip server, email geometricanalysiszulip@gmail.com.

Geometric Analysis Seminar. I run a local geometric analysis seminar at the University of Wollongong. Recent talks, abstracts, and venue details are on the seminar page.

Black Swan Academy of Mathematics logo

Black Swan Academy of Mathematics. The University of Wollongong’s School of Mathematics and Physics is an associate partner of the Black Swan Academy of Mathematics, which supports high-level mathematical research and education.

Australian Geometric Analysis and PDE Workshop at UOW. I co-organise this workshop as part of the GAP (Geometric Analysis and PDE) network. The timetable, talk titles, abstracts, and photographs from the recent workshop are on the workshop page.

Editorial work and governance

Editorial work. I serve on the editorial boards of the Journal of Evolution Equations, the Bulletin of the Australian Mathematical Society, and Transactions in Pure and Applied Mathematics. I have also served as a guest editor for the MATRIX Annals for special issues associated with programs I have organised at MATRIX.

Governance. I am Associate Head (Mathematics and Statistics) in the University of Wollongong’s School of Mathematics and Physics. I serve as the New South Wales representative on the national committee of the Australian Association of von Humboldt Fellows for 2025–2026, and as an ordinary member of the Council of the Australian Mathematical Society to the 2028 AGM. I chaired the School Education Committee in 2016–2021 and 2024–2025, leading curriculum reform and quality-assurance work, and have also served in roles including Academic Integrity Officer and Academic Program Director.

PhD supervision

I have supervised seven PhD students to completion: Scott Parkins (2017), Lachlan Macdonald (2019), Shuhui He (2019), Alex Mundey (2020), Yuhan Wu (2021), Sam Cuthbertson (2025), and Lachlann O’Donnell (2025). I currently supervise Brad Rice, Ben Whale, Vindula Kumaranayake, and Dinh Dat.

Interactive curve shortening flow

I forked Anthony Carapetis’ interactive curve-shortening-flow demonstration and made several small changes. Try it here.