/manager/Index ${session.getAttribute("locale")} 5 Zeta stars /manager/Repository/uon:6505 Wed 11 Apr 2018 14:40:36 AEST ]]> Pancyclicity and Cayley graphs on generalized dihedral groups /manager/Repository/uon:30205 Sat 24 Mar 2018 07:31:04 AEDT ]]> Finite time singularities for the locally constrained Willmore flow of surfaces /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 ]]>