| Abstract: |
| Euler's elastica is a critical point of the bending energy under the fixed length constraint, and its $L^p$-counterpart is called $p$-elastica. In this talk, I will present a characterization of the stability of $p$-elasticae under the pinned boundary condition. The key ingredient is a new ``cut-and-paste'' method that does not rely on the second variation but instead exploits the geometric invariance of the functional. This talk is based on joint work with Tatsuya Miura (Kyoto University). |
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