Name
Title | ||
|---|---|---|
Isometric Immersion of Surface with Negative Gauss Curvature and the Lax-Friedrichs Scheme |
Abstract | ||
|---|---|---|
The isometric immersion of two-dimensional Riemannian manifolds with negative Gauss curvature into the three-dimensional Euclidean space is considered through the Gauss-Codazzi equations for the first and second fundamental forms. The large L-infinity solution is obtained, which leads to a C-1,C-1 isometric immersion. The approximate solutions are constructed by the Lax-Friedrichs finite-difference scheme with the fractional step. The uniform estimate is established by studying the equations satisfied by the Riemann invariants and using the sign of the nonlinear part. The H-1 compactness is also derived. A compensated compactness framework is applied to obtain the existence of a large L-infinity solution to the Gauss-Codazzi equations for surfaces that are more general than those in the literature. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/15M1041766 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
isometric immersion,Gauss-Codazzi equations,Lax-Friedrichs scheme,L-infinity large solution,uniform estimate,compensated compactness | Nonlinear system,Mathematical analysis,Compact space,Euclidean space,Invariant (mathematics),Riemann hypothesis,Mathematics,Manifold,Gauss–Codazzi equations,Gaussian curvature | Journal |
Volume | Issue | ISSN |
48 | 3 | 0036-1410 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| wentao cao | 1 | 0 | 0.34 |
| Feimin Huang | 2 | 11 | 7.68 |
| dehua wang | 3 | 0 | 1.35 |