Presented by: 
Jürgen Jost (Max Planck Institute for Mathematical Sciences, Leipzig)
Date: 
Mon 18 Apr, 2:00 pm - 3:00 pm
Venue: 
Hawken Engineering Building (50), room N202

The famous result of Bernstein says that an entire minimal graph over the Euclidean plane is affine linear. This is one of the most striking results in nonlinear partial differential equations. Many mathematicians, including Moser, De Giorgi, Almgren, Simons, Chern, Yau have worked on extending this result to higher dimensions and codimensions. The result holds for codimension 1 and dimension < 8, but otherwise there exist counterexamples by Bombieri-de Giorgi-Giusti and Lawson-Osserman.

In this talk, I shall link the Bernstein problem to other concepts and structures in geometry and geometric analysis. More precisely, I shall reduce it to a problem about harmonic maps into spheres and Grassmann manifolds, and I shall show that the convex geometry of those spaces leads to new generalizations of the Bernstein theorem in any dimension and codimension.