4 papers
On the intersection of minimal hypersurfaces of
Renan Assimos
It is known since the work of Frankel that two compactly immersed minimal hypersurfaces in a manifold with positive Ricci curvature must have an intersection point. Several general…
Harmonic maps from surfaces of arbitrary genus into spheres
Renan Assimos, Jürgen Jost
We relate the existence problem of harmonic maps into to the convex geometry of . On one hand, this allows us to construct new examples of harmonic maps of degree 0 from…
Spherical Bernstein theorems for codimension 1 and 2
Renan Assimos, Jürgen 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 …
The Geometry of Maximum Principles and a Bernstein Theorem in Codimension 2
Renan Assimos, Jürgen Jost
Moser's Bernstein theorem \cite{moser61} says that an entire minimal graph of codimension 1 with bounded slope must be a hyperplane. An analogous result for arbitrary codimension i…