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arXiv · 1610.01649

Compensated Compactness in Banach Spaces and Weak Rigidity of Isometric Immersions of Manifolds

Gui-Qiang G. Chen·Siran Li
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Abstract

We present a compensated compactness theorem in Banach spaces established recently, whose formulation is originally motivated by the weak rigidity problem for isometric immersions of manifolds with lower regularity. As a corollary, a geometrically intrinsic div-curl lemma for tensor fields on Riemannian manifolds is obtained. Then we show how this intrinsic div-curl lemma can be employed to establish the global weak rigidity of the Gauss-Codazzi-Ricci equations, the Cartan formalism, and the corresponding isometric immersions of Riemannian submanifolds.

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Gui-Qiang G. Chen, Siran Li. 2016-10-01. Compensated Compactness in Banach Spaces and Weak Rigidity of Isometric Immersions of Manifolds. https://arxiv.org/abs/1610.01649

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