We present a compensated compactness theorem in Banach spaces establishedrecently, whose formulation is originally motivated by the weak rigidityproblem for isometric immersions of manifolds with lower regularity. As acorollary, a geometrically intrinsic div-curl lemma for tensor fields onRiemannian manifolds is obtained. Then we show how this intrinsic div-curllemma can be employed to establish the global weak rigidity of theGauss-Codazzi-Ricci equations, the Cartan formalism, and the correspondingisometric immersions of Riemannian submanifolds.
展开▼
