https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:35730 1-conforming Lagrange finite element spaces to approximate the solution. We prove a priori error estimates for our approach. Numerical results are presented for linear and quadratic finite element methods.]]> Wed 13 Nov 2019 09:53:30 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:42568 L² sense. Given a smooth initial curve we show that the solution to the flow exists for all time and, provided the length of the evolving curve remains bounded, smoothly converges to a multiplycovered circle. Moreover, we show that curves in any homotopy class with initially small L³‖k₈‖²₂ enjoy a uniform length bound under the flow, yielding the convergence result in these cases.]]> Thu 25 Aug 2022 11:40:14 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:44443 2-norm of the derivative of curvature with respect to arc length. We show that such curves between parallel lines converge exponentially in the C^∞ topology in infinite time to straight lines]]> Thu 13 Oct 2022 12:11:23 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:38428 2-norm of the gradient of the mean curvature. We show that such surfaces with small L²-norm of the second fundamental form and satisfying so-called flat boundary conditions are necessarily planar.]]> Thu 09 Sep 2021 15:23:32 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:35680 Mon 22 Aug 2022 09:48:35 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:40315 n+1. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature.]]> Mon 11 Jul 2022 09:13:58 AEST ]]>