A Willmore-Helfrich $L^2$-flow of curves with natural boundary conditions

Anna Dall'Acqua, Paola Pozzi
2014 Communications in analysis and geometry  
We consider regular open curves in R n with fixed boundary points and moving according to the L 2 -gradient flow for a generalization of the Helfrich functional. Natural boundary conditions are imposed along the evolution. More precisely, at the boundary the curvature vector is equal to the normal projection of a fixed given vector. A long-time existence result together with subconvergence to critical points is proven.
doi:10.4310/cag.2014.v22.n4.a2 fatcat:3ia6maxqg5cehftlpzadpx44yy