The Continuity of a surface as a function of its two fundamental forms

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Original languageEnglish
Pages (from-to)253-274
Journal / PublicationJournal des Mathematiques Pures et Appliquees
Issue number3
Publication statusPublished - 1 Mar 2003


The fundamental theorem of surface theory asserts that, if a field of positive definite symmetric matrices of order two and a field of symmetric matrices of order two together satisfy the Gauß and Codazzi-Mainardi equations in a connected and simply connected open subset of R2, then there exists a surface in R3 with these fields as its first and second fundamental forms and this surface is unique up to isometries in R3. We establish here that a surface defined in this fashion varies continuously as a function of its two fundamental forms, for certain natural topologies. © 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Research Area(s)

  • Differential geometry, Nonlinear shell theory, Surface theory