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On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus
Authors:Chunhe LI
Institution:School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
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 ?3.
Keywords:Alexandrov's positive annulus  Darboux equation  Gauss-Codazzi system  solvability
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