2019/10/30 by Renan Assimos, Jürgen Jost, Assimos, Renan +1
Computer Science · Mathematics · #53 XX #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1910.13966
openalex publication_date 2019/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We relate the existence problem of harmonic maps into S2 to the convex geometry of S2. On one hand, this allows us to construct new examples of harmonic maps of degree 0 from compact surfaces of arbitrary genus into S2. On the other hand, we produce new example of regions that do not contain closed geodesics (that is, harmonic maps from S1) but do contain images of harmonic maps from other domains. These regions can therefore not support a strictly convex function. Our construction builds upon an example of W. Kendall, and uses M. Struwe's heat flow approach for the existence of harmonic maps from surfaces.