Abstract
We extend the classical existence and uniqueness theory of Jenkins-Serrin $(H=0)$ and Spruck $(H>0)$ for the constant mean curvature equation over a domain in $R^2$, to domains in $H^2$ or $S^2$. This theory allows prescribed boundary data including plus or minus infinity on entire arcs of the boundary. Necessarily these arc must have curvature $+2H$ or $-2H$ with respect to the domain. We give necessary and sufficient conditions for existence in terms of so called admissible polygons. The key idea, as in previous proofs, is to study the "flux" of monotone increasing and decreasing sequences of solutions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.