2006/03/15 by Tristan Rivière, Tristan, Riviere · 4 citations
Mathematics · #35J60 #53A10 #53A30 #58E20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.math/0603380
openalex publication_date 2006/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without symmetries the well known conservation laws for harmonic maps into homogeneous spaces. From this form we can recover, without the use of moving frame, all the classical regularity results known for 2-dimensional conformally invariant non-linear elliptic PDE . It enable us also to establish new results. In particular we solve a conjecture by E.Heinz asserting that the solutions to the precribed bounded mean curvature equation in arbitrary manifolds are continuous.