Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities: A Brief Survey |
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| Authors: | Philippe G CIARLET Cristinel MARDARE and Sorin MARDARE |
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| Institution: | 1.Department of Mathematics,City University of Hong Kong,Kowloon,Hong Kong;2.Sorbonne Universités, Université Pierre et Marie Curie,Laboratoire Jacques-Louis Lions, CNRS-UMR 7598,Paris,France;3.Laboratoire de Mathématiques Rapha?l Salem UMR 6085 CNRS-Université de Rouen Avenue de l’Université,Saint-Etienne-du-Rouvray,France |
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| Abstract: | The authors discuss the existence and uniqueness up to isometries of E n of immersions ?: Ω ? R n → E n with prescribed metric tensor field (g ij ): Ω → S > n , and discuss the continuity of the mapping (g ij ) → ? defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping (g ij ) → ? can be obtained by means of nonlinear Korn inequalities is shown. |
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| Keywords: | Isometric immersions Nonlinear Korn inequalities Metric tensor |
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