带有平面边界凸曲面的无穷小刚性对偶问题的可解性  

Solvability of Infinitesimal Rigidity Dual Problem of Convex Surfaces with Planar Boundary

作　　者：程雪 李春和[1] CHENG Xue;LI Chunhe(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]电子科技大学数学科学学院,成都61173

出　　处：《数学年刊（A辑）》2023年第4期353-362,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金面上项目(No.12071059);四川省中央引导地方科技发展专项(No.2021ZYD0014)的资助.

摘　　要：本文重新讨论了一类带有平面边界的凸曲面的无穷小刚性问题.找到该线性化等距嵌入系统和齐次线性化Gauss-Codazzi系统之间的对偶关系.主要找到了齐次线性等距嵌入系统的对偶问题及对偶边界条件,并证明了其具有非平凡解,再次验证了该类凸曲面具有无穷小非刚性。This paper revisits the infinitesimal rigidity of a class of convex surfaces with planar boundary.A dual relation between this linearized isometric embedding system and the homogeneous linearized Gauss-Codazzi system is found.Mainly the dual problem and dual boundary condition of the homogeneous linear isometric embedded system is found,and its nontrivial solution is solved.Then the authors proved its infinitesimal nonrigidity again.

关 键 词：平面边界 对偶问题 凸曲面 无穷小刚性 

分 类 号：O186.1[理学—数学]