Area Bounds for Free Boundary Minimal Surfaces in a Geodesic Ball in the Sphere
Brian Freidin, Peter McGrath
TL;DR
This paper generalizes sharp area bounds for free boundary minimal surfaces from Euclidean space to higher-dimensional spheres, building on prior work by Brendle and Fraser-Schoen.
Contribution
It extends existing area bounds for free boundary minimal surfaces to higher dimensions within geodesic balls in the sphere.
Findings
Established new area bounds in higher dimensions
Connected results to prior Euclidean case work
Enhanced understanding of minimal surface geometry in spherical spaces
Abstract
We extend to higher dimensions earlier sharp bounds for the area of two dimensional free boundary minimal surfaces contained in a geodesic ball of the round sphere. This follows work of Brendle and Fraser-Schoen in the euclidean case.
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