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Differential Geometry and Continuum Mechanics pp 29–47Cite as

Global Isometric Embedding of Surfaces in \(\mathbb R^3\)

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 137))

Abstract

In this note, we give a short survey on the global isometric embedding of surfaces (2-dimensional Riemannian manifolds) in \(\mathbb R^3\). We will present associated partial differential equations for the isometric embedding and discuss their solvability. We will illustrate the important role of Gauss curvature in solving these equations.

The author acknowledges the support of NSF Grant DMS-1404596.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, 46556, USA

    Qing Han

  2. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Qing Han

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  1. Qing Han
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Correspondence to Qing Han .

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Editors and Affiliations

  1. Radcliffe Observatory Quarter, Mathematical Institute, Oxford, United Kingdom

    Gui-Qiang G. Chen

  2. Department of Mathematics and Statistics Livingstone Tower, University of Strathclyde, Glasgow, United Kingdom

    Michael Grinfeld

  3. School of Mathem. and Computer Science, Heriot-Watt University, Edinburgh, United Kingdom

    R. J. Knops

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Han, Q. (2015). Global Isometric Embedding of Surfaces in \(\mathbb R^3\) . In: Chen, GQ., Grinfeld, M., Knops, R. (eds) Differential Geometry and Continuum Mechanics. Springer Proceedings in Mathematics & Statistics, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-319-18573-6_2

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