Remarks on the generalised Calabi-Yau problem in higher codimension
Differential Geometry
2024-04-16 v1
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.
Cite
@article{arxiv.2404.08781,
title = {Remarks on the generalised Calabi-Yau problem in higher codimension},
author = {Renan Assimos and Balázs Márk Békési and Giuseppe Gentile},
journal= {arXiv preprint arXiv:2404.08781},
year = {2024}
}
Comments
28 pages, 6 figures