publications

publications by categories in reversed chronological order. generated by jekyll-scholar.

  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. 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.
  3. Miura, T., & Wheeler, G. (2025). Uniqueness and minimality of Euler’s elastica with monotone curvature. Journal of the European Mathematical Society.
  4. Miura, T., & Wheeler, G. (2025). The free elastic flow for closed planar curves. Journal of Functional Analysis, 111030.
  5. Rybka, P., & Wheeler, G. (2025). A classification of solitons for the surface diffusion flow of entire graphs. Physica D: Nonlinear Phenomena, 134702.
  6. 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
  7. Andrews, B., & Wheeler, G. (2025). The curve-lengthening flow in inversive geometry. ArXiv Preprint ArXiv:2502.17896.
  8. 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.
  9. 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.
  10. He, S., Whale, B., Wheeler, G., & Wheeler, V.-M. (2025). A curvature flow approach to dorsal closure modelling. ArXiv Preprint ArXiv:2507.12088.
  11. Andrews, B., & Wheeler, G. (2025). On the planar free elastic flow with small oscillation of curvature. ArXiv Preprint ArXiv:2509.11129.
  12. Wheeler, G., & Wheeler, V.-M. (2024). Curve diffusion and straightening flows on parallel lines. Communications in Analysis and Geometry.
  13. 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.
  14. 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.
  15. Cuthbertson, S., Wheeler, G., & Wheeler, V. (2024). A curvature flow that deforms curves to an embedded target. ArXiv Preprint ArXiv:2411.18951.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. McCoy, J. A., Schrader, P., & Wheeler, G. (2023). Representation formulae for higher order curvature flows. Journal of Differential Equations, 344, 1–43.
  22. Dean, B. A., Mundy, T., Price, O., Kennedy, M. A., Wheeler, G., Sheridan, L., & Iskra, L. (2023). Resourcing and recognition: Academics’ perceptions of challenges experienced embedding work-integrated learning in the curriculum. International Journal on Work Integrated Learning.
  23. 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.
  24. Mccoy, J. A., Wheeler, G. E., & Wu, Y. (2022). A Length-Constrained Ideal Curve Flow. The Quarterly Journal of Mathematics, 73(2), 685–699.
  25. 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.
  26. Wheeler, G. (2021). Convergence for global curve diffusion flows. Mathematics In Engineering, 4(1), 1.
  27. Wheeler, G., & Wheeler, V.-M. (2020). Mean curvature flow with free boundary–Type 2 singularities. Mathematische Nachrichten, 293(4), 794–813.
  28. McCoy, J., Wheeler, G., & Wu, Y. (2020). A sixth order flow of plane curves with boundary conditions. Tohoku Mathematical Journal, 72(3), 379–393.
  29. Andrews, B., McCoy, J., Wheeler, G., & Wheeler, V.-M. (2020). Closed ideal planar curves. Geometry & Topology, 24(2), 1019–1049.
  30. 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.
  31. McCoy, J., & Wheeler, G. (2020). A rigidity theorem for ideal surfaces with flat boundary. Annals of Global Analysis and Geometry, 57(1), 1–13.
  32. Wheeler, G., & Wheeler, V.-M. (2019). Minimal hypersurfaces in the ball with free boundary. Differential Geometry and Its Applications, 62, 120–127.
  33. 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.
  34. Parkins, S., & Wheeler, G. (2019). The anisotropic polyharmonic curve flow for closed plane curves. Calculus of Variations and Partial Differential Equations, 58(2), 70.
  35. 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.
  36. He, S., Wheeler, G., & Wheeler, V.-M. (2019). On a curvature flow model for embryonic epidermal wound healing. Nonlinear Analysis, 189, 111581.
  37. McCoy, J., Wheeler, G., & Wu, Y. (2019). A sixth order curvature flow of plane curves with boundary conditions. 2017 MATRIX Annals, 213–221.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42. McCoy, J., Parkins, S., & Wheeler, G. (2017). The geometric triharmonic heat flow of immersed surfaces near spheres. Nonlinear Analysis, 161, 44–86.
  43. 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.
  44. 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.
  45. Drugan, G., Lee, H., & Wheeler, G. (2016). Solitons for the inverse mean curvature flow. Pacific Journal of Mathematics, 284(2), 309–326.
  46. Parkins, S., & Wheeler, G. (2016). The polyharmonic heat flow of closed plane curves. Journal of Mathematical Analysis and Applications, 439(2), 608–633.
  47. 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.
  48. 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.
  49. 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.
  50. 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.
  51. McCoy, J., & Wheeler, G. (2013). A classification theorem for Helfrich surfaces. Mathematische Annalen, 357, 1485–1508.
  52. 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.
  53. Wheeler, G. (2013). Chen’s conjecture and \varepsilon-superbiharmonic submanifolds of Riemannian manifolds. International Journal of Mathematics, 24(04), 1350028.
  54. Wheeler, V.-M., McCoy, J. A., Wheeler, G., & Sharples, J. J. (2013). Curvature flows and barriers in fire front modelling. MODSIM.
  55. Sharples, J. J., Towers, I. N., Wheeler, G., Wheeler, V.-M., & McCoy, J. A. (2013). Modelling fire line merging using plane curature flow. MODSIM.
  56. Wheeler, G. (2012). Surface diffusion flow near spheres. Calculus of Variations and Partial Differential Equations, 44(1), 131–151.
  57. Wheeler, G. (2012). On the curve diffusion flow of closed plane curves. Annali Di Matematica Pura Ed Applicata, 1–20.
  58. Wheeler, G. (2011). Lifespan theorem for simple constrained surface diffusion flows. Journal of Mathematical Analysis and Applications, 375(2), 685–698.
  59. McCoy, J., Wheeler, G., & Williams, G. (2011). Lifespan theorem for constrained surface diffusion flows. Mathematische Zeitschrift, 269(1), 147–178.
  60. Wheeler, G. (2010). Fourth order geometric evolution equations. Bulletin of the Australian Mathematical Society, 82(3), 523–524.
  61. Bunder, M. W., Tognetti, K. P., & Wheeler, G. E. (2008). On binary reflected Gray codes and functions. Discrete Mathematics, 308(9), 1690–1700.
  62. Wheeler, G. (2008). Shi’s local estimates. Oberwolfach Reports.
  63. Wheeler, G. E., Safavi-Naini, R., & Sheppard, N. P. (2005). Weighted segmented digital watermarking. Digital Watermarking: Third International Workshop, IWDW 2004, Seoul, South Korea, October 30-November 1, 2004, Revised Selected Papers 3, 89–100.