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| Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities: A Brief Survey |
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Citation： |
Philippe G. CIARLET,Cristinel MARDARE,Sorin MARDARE.Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities: A Brief Survey[J].Chinese Annals of Mathematics B,2017,38(1):253~280 |
| Page view： 731
Net amount： 700 |
Authors： |
Philippe G. CIARLET; Cristinel MARDARE;Sorin MARDARE |
Foundation： |
This work was supported by a grant from the Research
Grants Council of the Hong Kong Special Administration Region, China
(Nos.9041637, CiyuU100711). |
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| Abstract： |
The authors discuss the existence and uniqueness up to isometries of
$\r^n$ of immersions $\bph:\Om\subset \mathbb{R}^n\to \r^n$ with
prescribed metric tensor field $(g_{ij}):\Om\to\s^n_>$, and
discuss the continuity of the mapping $(g_{ij})\to\bph$ 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 $(g_{ij})\to\bph$
can be obtained by means of nonlinear Korn inequalities is shown. |
Keywords： |
Isometric immersions, Nonlinear Korn inequalities, Metric tensor |
Classification： |
74B20, 53C24 |
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