Half-Space Intersection Properties for Minimal Hypersurfaces
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12220_2025_2006_ReferencePDF.pdf
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Author(s)
Naff, Keaton
Zhu, Jonathan J.
Date Issued
April 16, 2025
Journal
The Journal of Geometric Analysis
Publisher
Springer US
Citation
Naff, K., Zhu, J.J. Half-Space Intersection Properties for Minimal Hypersurfaces. J Geom Anal 35, 172 (2025).
Version
Author's final manuscript
Abstract
We prove “half-space” intersection properties in three settings: the hemisphere, half-geodesic balls in space forms, and certain subsets of Gaussian space. For instance, any two embedded minimal hypersurfaces in the sphere must intersect in every closed hemisphere. Two approaches are developed: one using classifications of stable minimal hypersurfaces, and the second using conformal change and comparison geometry for α -Bakry-Émery-Ricci curvature. Our methods yield the analogous intersection properties for free boundary minimal hypersurfaces in space form balls, even when the interior or boundary curvature may be negative. Finally, Colding and Minicozzi recently showed that any two embedded shrinkers of dimension n must intersect in a large enough Euclidean ball of radius R(n). We show that R ( n ) ≤ 2 n.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s12220-025-02006-3
