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.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We give an overview of the classification of networks in the plane with at most two triple junctions with the property that under the motion by curvature they are self-similarly shrinking. After the contributions in [7, 9, 20], such a classification was completed in the recent work in [4] (see also [3]), proving that there are no self-shrinking networks homeomorphic to the Greek “theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees. We present the main geometric ideas behind the work [4]. We also briefly introduce our work in progress in the higher-dimensional case of networks of surfaces in R3.
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We compute the evolution equation of the Cotton and the Bach tensor under the Ricci flow of a Riemannian manifold, with particular attention to the three dimensional case, and we discuss some applications.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.