Abstract
AbstractWe consider the class of ‐dimensional surfaces in that intersect orthogonally along the boundary. A piece of an affine ‐plane in is called an orthogonal slice. We prove estimates for the area by the integral of the second fundamental form in three cases: first, when admits no orthogonal slices, second for if all orthogonal slices are topological disks, and finally, for all if the surfaces are confined to a neighborhood of . The orthogonality constraint has a weak formulation for curvature varifolds. We classify those varifolds of vanishing curvature. As an application, we prove for any the existence of an orthogonal 2‐varifold that minimizes the curvature in the integer rectifiable class.
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.
