Abstract
In this paper, we investigate the various aspects of normal hyperbolic mean curvature flow by LeFloch and Smoczyk. It is remarkable that the equation admits the null condition in three-dimensional case and only satisfies the first null condition when [Formula: see text]. Based on the interesting findings, we can obtain the results of global existence of smooth solutions, as well as the stability of hyperplanes under this flow when [Formula: see text], which relates to the famous Bernstein theorem. Some explicit solutions for this flow have been also derived. It should be emphasized that the null structures of this hyperbolic mean curvature flow have not been found before.
Sign-in/Register to access full text options 
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.
