A Surface is a Continuous Function of its Fundamental Forms

Events

Abstract

It is well known that a surface can be recovered from its two fundamental forms if they satisfy the Gauss and Codazzi-Mainardi compatibility equations on a simply-connected open set, in which case the surface is uniquely determined up to isometric equivalence.
It is less known that in this case the surface becomes a continuous function of its fundamental forms, again up to isometric equivalence, for various topologies, such as the Fréchet topology of continuously differentiable functions, or those corresponding to various Sobolev norms.
In this talk, we will review such continuity results obtained during the past fifteen years, as well as their close relations to nonlinear Korn inequalities on a surface.
We will also mention potential applications of such results, such as the intrinsic approach to nonlinear shell theory, where the unknowns are the fundamental forms of the deformed middle surface of a shell.
All the needed notions from the differential geometry of surfaces will be first carefully reviewed, so as to make the lecture as self-contained as possible.

Speaker

Professor Philippe Ciarlet

Professor Ciarlet is Emeritus Professor of Sorbonne-Université (Paris), Emeritus Professor of City University of Hong Kong, and a Senior Fellow of the Hong Kong Institute for Advanced Study of City University of Hong Kong (HKIAS). Professor Ciarlet is an Officer in the National Order of the Legion of Honor of France. He is a Member of the French Academy of Sciences, of the French Academy of Technologies, of the Academia Europaea, of the European Academy of Sciences, of the Romanian Academy, of the World Academy of Sciences (TWAS), of the National Academy of Sciences of India, of the Academy of Sciences of Hong Kong, and a Foreign Member of the Chinese Academy of Sciences.
Professor Ciarlet is well-kown for his numerous fundamental contributions to the mathematical analysis of the finite element method, to the mathematical theory of elasticity, plates, and shells, and to nonlinear Korn inequalities on surfaces.
In addition to having published more than 200 research papers, he has written seventeen books, which include well-known texts such as The Finite Element Method for Elliptic Problems, Introduction to Numerical Linear Algebra and Optimization, Mathematical Elasticity (three Volumes), and Linear and Nonlinear Functional Analysis with Applications – Second Edition.