Geometry Seminar: R. Assimos Martin (Leibniz Universität Hannover)
Geometry Seminar (Geometric Analysis)
Speaker: Renan Assimos Martin (Leibniz Universität Hannover)
Title: Remarks on the Calabi-Yau problem in higher codimension
Speaker: Renan Assimos Martin (Leibniz Universität Hannover)
Title: Remarks on the Calabi-Yau problem in higher codimension
Abstract: By introducing a more flexible notion of convexity, we obtain a new Omori-Yau maximum principle for harmonic maps. In the spirit of the Calabi-Yau conjectures, this principle is more suitable for studying the unboundedness of certain totally geodesic projections of minimal submanifolds of higher codimension. We further explore this maximum principle by applying it to conformal maps, harmonic maps into Cartan-Hadamard manifolds, as well as cone, wedge and halfspace theorems.