Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities : A Brief Survey

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)253-280
Journal / PublicationChinese Annals of Mathematics. Series B
Issue number1
Online published5 Jan 2017
Publication statusPublished - Jan 2017


The authors discuss the existence and uniqueness up to isometries of En of immersions φ : Ω ⊂ Rn → En with prescribed metric tensor field (gij) : Ω → S>n, and discuss the continuity of the mapping (gij) → Φ 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 (gij) → Φ can be obtained by means of nonlinear Korn inequalities is shown.

Research Area(s)

  • Isometric immersions, Metric tensor, Nonlinear Korn inequalities