Abstract
In this paper, we mainly consider the relative isoperimetric inequalities for minimal submanifolds with free boundary. We first generalize ideas of restricted normal cones introduced by Choe-Ghomi-Ritoré in [10] and obtain an optimal area estimate for generalized restricted normal cones. This area estimate, together with the ABP method of Cabré in [5], provides a new proof of the relative isoperimetric inequality obtained by Choe-Ghomi-Ritoré in [11]. Furthermore, we use this estimate and the idea of Brendle in his recent work [3] to obtain a relative isoperimetric inequality for minimal submanifolds with free boundary on a convex support surface in Rn+m, which is optimal and gives an affirmative answer to an open problem proposed by Choe in [9], Open Problem 12.6, when the codimension m≤2.
Submitted Version (
Free)
Published Version
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.
