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| On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus |
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Citation： |
Chunhe LI.On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus[J].Chinese Annals of Mathematics B,2013,34(3):435~454 |
| Page view： 3080
Net amount： 2562 |
Authors： |
Chunhe LI; |
Foundation： |
the National Natural Science Foundation of China (No. 11101068), the Fundamental Research Funds for the Central Universities (No. ZYGX2010J109) and the Sichuan Youth Science and Technology Foundation (No. 2011JQ0003). |
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| Abstract： |
In the present paper, the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given. In the meantime, the solvability of a relevant linearized Darboux equation is given. The equations are arising in a geometric problem which is
concerned with the realization of the Alexandrov's positive annulus in $\mathbb{R}^3$. |
Keywords： |
Alexandrov's positive annulus, Darboux equation, Gauss-Codazzi system, solvability |
Classification： |
53C24, 53C45 |
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