A survey of the elastic flow of curves and networks
- Resource Type
- Authors
- Alessandra Pluda; Marco Pozzetta; Carlo Mantegazza
- Source
- Subject
- Mathematics - Differential Geometry
General Mathematics
010102 general mathematics
Mathematical analysis
State (functional analysis)
01 natural sciences
010101 applied mathematics
Section (fiber bundle)
Mathematics - Analysis of PDEs
Flow (mathematics)
Differential Geometry (math.DG)
Convergence (routing)
FOS: Mathematics
0101 mathematics
Mathematics
Analysis of PDEs (math.AP)
- Language
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and smooth convergence to critical points of the solution of the elastic flow of closed curves in $${\mathbb {R}}^2$$ R 2 . In the last section of the paper we also discuss a list of open problems.