Abstract
LetM be a Hadamard manifold with all sectional curvatures bounded above by some negative constant. A well-known lemma essentially due to M. Morse states that every quasigeodesic segment inM lies within an a priori bounded distance from the geodesic arc connecting its endpoints. In this paper we establish an analogue of this fact for quasiminimizing surfaces in all dimensions and codimensions; the only additional requirement is that the sectional curvatures ofM be bounded from below as well. We apply this estimate to obtain new solutions to the asymptotic Plateau problem in various settings.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
