A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds

2018/06/28 by Volker Branding, Yong Luo, Branding, Volker +1
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1806.11441

openalex publication_date 2018/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension \(m=dim M≥ 3\) with infinite volume that admit an Euclidean type Sobolev inequality into general Riemannian manifolds by assuming finiteness of ‖τ(ϕ)‖_L^p(M), p>1 and smallness of ‖dϕ‖_L^m(M). This is an improvement of a recent result of the first named author, where he assumed 2

Citations

• Harmonic Mappings of Riemannian Manifolds

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