Wedge product theorem in compensated compactness theory with critical exponents on Riemannian manifolds

2023/07/24 by Li, Siran
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.13175

Abstract

We formulate and prove compensated compactness theorems concerning the limiting behaviour of wedge products of weakly convergent differential forms on closed Riemannian manifolds. The case of critical regularity exponents is considered, which goes beyond the regularity regime entailed by Hölder's inequality. Implications on the weak continuity of L^p-extrinsic geometry of isometric immersions of Riemannian manifolds are discussed.

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