Geodesics and Isometric Immersions in Kirigami

：韩青（美国Notre Dame大学）
：2021-05-11 10:00
：腾讯会议ID：866 484 064（线上）

报告人：韩青（美国Notre Dame大学）

时  间：5月11日上午10:00

地  点：腾讯会议ID：866 484 064（线上）

内容摘要:

Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled and limited by the presence of cuts that serve to guide the possible non-planar deformations. Inspired by the geometry of this art form, we ask two questions: (i) What is the shortest path between points at which forces are applied? (ii) What is the nature of the ultimate shape of the sheet when it is strongly stretched? Mathematically, these questions are related to the nature and form of geodesics in the Euclidean plane with linear obstructions (cuts), and the nature and form of isometric immersions of the sheet with cuts when it can be folded on itself. We provide a constructive proof that the geodesic connecting any two points in the plane is piecewise polygonal. We then prove that the family of polygonal geodesics can be simultaneously rectified into a straight line by flat-folding the sheet so that its configuration is a (non-unique) piecewise affine planar isometric immersion. The talk is based on joint works with M. Lewicka and L. Mahadevan.

个人简介：

韩青，国际著名的偏微分方程和几何分析专家，美国圣母大学教授。在等距嵌入、Monge-Ampere方程、调和函数的零点集和奇异集、退化方程，极小曲面方程、Yamabe方程的渐近行为等方面做出了一系列原创性的重要研究成果。

 

联系人：夏超