Weak Continuity of the Gauss-Codazzi-Ricci System for Isometric Embedding
| dc.creator | Chen, Gui-Qiang | |
| dc.creator | Slemrod, Marshall | |
| dc.creator | Wang, Dehua | |
| dc.date | 2009-04-23 | |
| dc.date.accessioned | 2026-07-07T13:07:50Z | |
| dc.date.available | 2026-07-07T13:07:50Z | |
| dc.description | We establish the weak continuity of the Gauss-Coddazi-Ricci system for isometric embedding with respect to the uniform $L^p$-bounded solution sequence for $p>2$, which implies that the weak limit of the isometric embeddings of the manifold is still an isometric embedding. More generally, we establish a compensated compactness framework for the Gauss-Codazzi-Ricci system in differential geometry. That is, given any sequence of approximate solutions to this system which is uniformly bounded in $L^2$ and has reasonable bounds on the errors made in the approximation (the errors are confined in a compact subset of $H^{-1}_{\text{loc}}$), then the approximating sequence has a weakly convergent subsequence whose limit is a solution of the Gauss-Codazzi-Ricci system. Furthermore, a minimizing problem is proposed as a selection criterion. For these, no restriction on the Riemann curvature tensor is made. | |
| dc.identifier | https://arxiv.org/abs/0904.3583 | |
| dc.identifier | http://arxiv.org/abs/0904.3583 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228223 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C42, 53C21, 53C45, 35L65, 35M20, 35B35 | |
| dc.title | Weak Continuity of the Gauss-Codazzi-Ricci System for Isometric Embedding | |
| dc.type | text |