Título: The geometry of the maximum principle and a spherical Bernstein theorem by B. Solomon

Palestrante: Renan Assimos Martins (Hannover)
Data: 27/07/2021
Horário: 14:00h
Local: Transmissão online

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Resumo: Joint work with J. Jost: A result of B.Solomon (On the Gauss map of an area-minimizing hypersurface. 1984. Journal of Differential Geometry, 19(1), 221-232.) says that a compact minimal hypersurface $M^k$ of the sphere $S^{k+1}$ with $H^1(M)=0$, whose Gauss map omits a neighborhood of an $S^{k−1}$ equator, is totally geodesic in $S^{k+1}$. In this talk, I will present a new proof strategy for Solomon's theorem which allows us to obtain analogous results for higher codimensions. If time permits, we sketch the proof for codimension 2 compact minimal submanifolds of $S^{k+1}$.