Geometric PDE and Applied Analysis Seminar (October 12, 2023)

Title: Li-Yau type inequality for the p-bending energy

Speaker: Dr. Kensuke Yoshizawa (Kyushu University)

Abstract: Li-Yau obtained the sharp inequality that the Willmore energy of a closed surface is bounded below by \(4\pi\) times multiplicity. Its one-dimensional counterpart involving the so-called bending energy for planar curves has also been studied. In this talk, we generalize the bending energy to the \(p\)-bending energy for \(p>1\) to discuss analogous results, and then reveal some new phenomena on its optimality arising from the generality of \(p>1\). This talk is based on a joint work with Prof. Tatsuya Miura (Tokyo Institute of Technology).