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Some minimization problems for planar networks of elastic curves

100%

Dall’Acqua A., Pluda A.

Geometric Flows

2017

tom 2

nr 1

In this note we announce some results that will appear in [6] on the minimization of the functional F(Γ) = ∫Γk2 + 1 ds, where Γ is a network of three curves with fixed equal angles at the two junctions. The informal description of the results is accompanied by a partial review of the theory of elasticae and a diffuse discussion about the onset of interesting variants of the original problem passing from curves to networks. The considered energy functional F is given by the elastic energy and a term that penalize the total length of the network.We will show that penalizing the length is tantamount to fix it. The paper is concluded with the explicit computation of the penalized elastic energy of the “Figure Eight”, namely the unique closed elastica with self-intersections (see Figure 1).

Motion by curvature of networks with two triple junctions

81%

Mantegazza C., Novaga M., Pluda A.

Geometric Flows

2017

tom 2

nr 1

We consider the evolution by curvature of a general embedded network with two triple junctions. We classify the possible singularities and we discuss the long time existence of the evolution.

Ograniczanie wyników

2 Geometric Flows

2 Pluda A.

1 Dall’Acqua A.

1 Mantegazza C.

1 Novaga M.

1 2017

1 2016

Wyniki wyszukiwania

Some minimization problems for planar networks of elastic curves

Motion by curvature of networks with two triple junctions