Project Details
Projekt
Flow of elastic networks
Subject Area
Mathematics
Term
from 2018 to 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 404870139
The main topic of this project is the evolution of elastic networks. A typical example of a planar network is the ``Mercedes-Benz''-symbol of three curves joined at one point and with the other endpoints lying on a given boundary. Another example is that of a theta-network, where three curves are joint together in such a way that they meet at two triple-points. Networks configurations are interesting in applications since they naturally arise in phase transitions. Evolution of networks of three or more curves under mean curvature flow has received a lot of attentions in recent years. A lot of interesting and yet unexplored mathematical questions arise when one looks at higher order flows, such as the elastic one, that is the gradient flow of the elastic energy. Previous works of the applicants especially focus on longtime existence results for (single) open elastic curves under various choices of boundary conditions and length control. It is planned to employ this knowledge to better understand and describe higher order flows in the network setting.
DFG Programme
Research Grants
International Connection
Taiwan
Partner Organisation
National Science and Technology Council (NSTC)
Cooperation Partner
Professor Chun-Chi Lin, Ph.D.
