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The semi-global isometric embedding of surfaces with curvature changing signs stably


Author: Wentao Cao
Journal: Proc. Amer. Math. Soc. 147 (2019), 4343-4353
MSC (2010): Primary 35M12, 53A05, 53C21
DOI: https://doi.org/10.1090/proc/14597
Published electronically: May 17, 2019
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Abstract: 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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Additional Information

Wentao Cao
Affiliation: Institute für mathematik, Universität Leipzig, D-04109, Leipzig, Germany
Email: wentao.cao@math.uni-leipzig.de

DOI: https://doi.org/10.1090/proc/14597
Keywords: Isometric embedding, semi-global, equation of mixed type, the Darboux equation, stably, symmetric positive system.
Received by editor(s): April 6, 2018
Received by editor(s) in revised form: January 11, 2019
Published electronically: May 17, 2019
Additional Notes: The research was supported by the ERC Grant Agreement No. 724298.
Communicated by: Jiaping Wang
Article copyright: © Copyright 2019 American Mathematical Society