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| DARBOUX EQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIANMANIFOLDS WITH NONNEGATIVE CURVATURE IN R^3 |
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Citation： |
Hong Jiaxing.DARBOUX EQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIANMANIFOLDS WITH NONNEGATIVE CURVATURE IN R^3[J].Chinese Annals of Mathematics B,1999,20(2):123~136 |
| Page view： 1279
Net amount： 755 |
Authors： |
Hong Jiaxing; |
Foundation： |
the National Natural Science
Foundation of China |
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| Abstract： |
The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate
on the boundary is contained. As some applications the smooth isometric embeddings of positively and nonnegatively curved disks into $R^3$ are constructed. |
Keywords： |
Darboux equation, Isometric embedding, Riemannian
manifold, Nonnegative curvature |
Classification： |
35J60, 53C21, 53C42 |
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