https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 A regularized gradient flow for the p-elastic energy https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:51628 Tue 12 Sep 2023 20:08:20 AEST ]]> Finite time singularities for the locally constrained Willmore flow of surfaces https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:40250 L²-gradient flow of the functional Wλ1,λ2, which is the the sum of the Willmore energy, λ1-weighted surface area, and λ2-weighted enclosed volume, for surfaces immersed in ℝ³. This coincides with the Helfrich functional with zero 'spontaneous curvature'. Our first results are a concentration-compactness alternative and interior estimates for the flow. For initial data with small energy, we prove preservation of embeddedness, and by directly estimating the Euler-Lagrange operator from below in L² we obtain that the maximal time of existence is finite. Combining this result with the analysis of a suitable blowup allows us to show that for such initial data the flow contracts to a round point in finite time.]]> Fri 08 Jul 2022 13:28:33 AEST ]]>