On the linearized Darboux equation arising in isometric embedding of the Alexandrov positive annulus

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 ℝ³.

Keywords

Alexandrov’s positive annulus / Darboux equation / Gauss-Codazzi system / solvability

References

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