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Centre for Geometric Analysis Seminar Series
June 13, 2019 @ 10:00 am - July 12, 2019 @ 12:00 pm
Prof Shinya Okabe (Tohoku University Japan)
The obstacle problem for the elastic flow defined on the planar open curve
In this talk, we consider the elastic flow defined on planar graphed curves with obstacle. Formally the problem is regarded as the L^2-gradient flow for the elastic energy with obstacle constraint. However, due to the obstacle constraint, it is not so clear that solutions to the obstacle problem have a gradient structure for the elastic energy. In this talk, we prove the existence of local-in-time weak solutions via minimizing movements. Moreover, we show a gradient structure of the elastic energy of the weak solutions.This talk is based on a joint work with Kensuke Yoshizawa of Tohoku University.
Prof Tatsuya Miura (Tokyo Institute of Technology Japan)
Rigidity results for optimal elastic curves via a geometric approach
In this talk we study elastic curves, which are critical points of bending energy. In general there may be (infinitely) many critical points for a given boundary condition, and hence in order to detect local or global minimizers we usually need to calculate the second variation or compare their energy. The goal of this talk is to introduce our new geometric approach that bypasses calculation of the second variation but implies several necessary conditions on critical points for being locally or globally optimal. Our method not only retrieves Sachkov’s results for planar elasticae, but also can be applied to more general problems, e.g. spatial elastic curves.