The semi-global isometric embedding of surfaces with curvature changing signs stably
W Cao - Proceedings of the American Mathematical Society, 2019 - JSTOR
Proceedings of the American Mathematical Society, 2019•JSTOR
… Then Han improved the regularity of the embedding in [8], and later he also showed the
existence of local isometric embedding when the Gaussian curvature changes signs stably; ie,
K vanishes at finite order across a curve in [9]. For the semi-global isometric embedding, Dong
first showed that there exists an isometric embedding parametrized on [0, 2π] × [−δ, δ] mapping
into R3 in [4] provided that the positive constant δ is small enough and K satisfies … In the
present paper, we gain a semi-global isometric embedding for the case where the Gaussian …
existence of local isometric embedding when the Gaussian curvature changes signs stably; ie,
K vanishes at finite order across a curve in [9]. For the semi-global isometric embedding, Dong
first showed that there exists an isometric embedding parametrized on [0, 2π] × [−δ, δ] mapping
into R3 in [4] provided that the positive constant δ is small enough and K satisfies … In the
present paper, we gain a semi-global isometric embedding for the case where the Gaussian …
A semi-global isometric embedding of abstract surfaces with Gaussian curvature changing signs of any finite order is obtained through solving the Darboux equation.
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