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Geometric Analysis Seminar

Area estimates and intersection properties for minimal hypersurfaces in space forms

Keaton Naff

Location:  Hill-705
Date & time: Tuesday, 05 March 2024 at 2:50PM - 3:50PM

In this talk, I wish to discuss recent work (joint with Jonathan J. Zhu) on area estimates for minimal submanifolds and ``half-space" Frankel properties for minimal hypersurfaces in space forms. In the first setting, we will discuss sharp area estimates for minimal submanifolds in the curved space forms which pass through a prescribed point (building on work of Brendle-Hung). Our work settles the question in the hyperbolic setting, but leaves open an interesting outstanding question in the sphere. This leads naturally to the question of stability of minimal submanifolds in the hemisphere and in this direction we will demonstrate a Frankel property for the hemisphere (and other related settings).