New nonlinear estimates for surfaces in terms of their fundamental forms

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Original languageEnglish
Pages (from-to)226-231
Journal / PublicationComptes Rendus Mathematique
Issue number2
Online published1 Feb 2017
Publication statusPublished - Feb 2017


We establish several estimates of the distance between two surfaces immersed in the three-dimensional Euclidean space in terms of the distance between their fundamental forms, measured in various Sobolev norms. These estimates, which can be seen as nonlinear versions of linear Korn inequalities on a surface appearing in the theory of linearly elastic shells, generalize in particular the nonlinear Korn inequality established in 2005 by P. G. Ciarlet, L. Gratie, and C. Mardare.