Alessandra Pluda
Elastic curves and surfaces
A. Dall'Acqua, A. Pluda Some minimization problems for planar networks of elastic curves;
A. Dall'Acqua, M. Novaga, A. Pluda Minimal elastic networks;
G. Del Nin, A. Pluda, M.Pozzetta Degenerate elastic networks;
H.Garcke, J.Menzel, A.Pluda Willmore flow of planar networks;
H.Garcke, J.Menzel, A.Pluda Long time existence of solutions to an elastic flow of networks;
C. Mantegazza, A. Pluda, M.Pozzetta A survey of the elastic flow of curves and networks;
M. Novaga, A. Pluda Elastic networks: statics and dynamics;
C.Brand, G.Dolzmann, A. Pluda Variational models for the interaction of surfactants with curvature - existence and regularity of minimizers in the case of flexible curves
Figure: Examples of Theta-networks with equal angles at the junctions.
Figure: The circle and the ``Figure Eight".
Figure: A Theta-network and a Triod.
References
Calibrations for the Steiner Problem, minimal partitions and the mailing problem
M.Carioni, A.Pluda, Calibrations for minimal networks in a covering space setting.
M.Carioni, A.Pluda, On different notions of calibrations for minimal partitions and minimal networks in R^2
M.Carioni, A.Marchese, A.Massaccesi, A.Pluda, R.Tione The oriented mailing problem and its convex relaxation
A.Pluda, M.Pozzetta Minimizing properties of networks via global and local calibrations
Figure: Idea of the covering.
Figure: A minimizer for the vertices of the square and its calibration.
References
Motion by curvature of networks
A.Pluda, Evolution of spoon-shaped networks;
C.Mantegazza, M.Novaga, A.Pluda, Motion by curvature of networks with two triple junctions;
C.Mantegazza, M.Novaga, A.Pluda, F.Schulze, Evolution of networks with multiple junctions;
M.Gößwein, J.Menzel, A.Pluda, Existence and uniqueness of the motion by curvature of regular networks;
J. Lira, R.Mazzeo, A.Pluda, M.Saez Short-time existence for the network flow;
C.Mantegazza, M.Novaga, A.Pluda, Lectures on curvature flow of networks.
C.Mantegazza, M.Novaga, A.Pluda, Type-0 singularities in the network flow - Evolution of trees
A.Pluda, M.Pozzetta Lojasiewicz-Simon inequalities for minimal networks: stability and convergence
A.Pluda, M.Pozzetta On the uniqueness of nondegenerate blowups for the motion by curvature of networks
References
Spines of minimal length
B.Martelli, M.Novaga, A.Pluda, S.Riolo, Spines of minimal length.
Figure: A spine of a surface of genus 1 and a surface of genus 2.
Figure: The minimal spines in some oriented tori having additional symmetries. As we pass from rectangular to thin rhombic, we find 2, 1, 2, 1, and then 3 spines up to orientation-preserving isometries. They reduce to 1, 1, 2, 1, 2 up to all isometries, including orientation-reversing ones.Rectangles and rhombi that are thinner (ie longer) than the ones shown here have additional minimal spines that wind around the thin part.
References
