On a spherical Bernstein theorem by B. Solomon

Abstract: 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 $S^{k+1}$.

mathematical physicsanalysis of PDEsdifferential geometryfunctional analysismetric geometry

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php