Incompatible elasticity and the immersion of non-flat Riemannian manifolds in Euclidean space

DOI10.1007/s11856-011-0187-1zbMath1260.53069OpenAlexW2007174367WikidataQ115377693 ScholiaQ115377693MaRDI QIDQ1760395

Yossi Shamai, Raz Kupferman

Publication date: 13 November 2012

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-011-0187-1

zbMATH Keywords

coercivityRiemannian manifoldscalar curvatureimmersionGauss curvaturelower bound estimatesincompatible elasticityelastic energy integral

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20) Differential geometric aspects of harmonic maps (53C43) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Elastic materials (74B99)

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Cites Work

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• On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
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