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This content will become publicly available on June 1, 2026

Title: Half-Space Intersection Properties for Minimal Hypersurfaces
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 $$\alpha$$-Bakry-\'{E}mery-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 $$R(n) \leq 2 \sqrt{n}$$.  more » « less
Award ID(s):
2103265
PAR ID:
10635546
Author(s) / Creator(s):
;
Publisher / Repository:
Springer Nature
Date Published:
Journal Name:
The Journal of Geometric Analysis
Volume:
35
Issue:
6
ISSN:
1050-6926
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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