Stable proper biharmonic maps in Euclidean spheres
Abstract
We construct an explicit family of stable proper weak biharmonic maps from the closed Euclidean unit ball B m , m ≥ 5, to Euclidean spheres.To the best of the authors knowledge this is the first example of a stable proper weak biharmonic map from a compact domain.To achieve our result we first establish the second variation formula of the bienergy for maps from the unit ball into a Euclidean sphere.Employing this result, we examine the stability of the proper weak biharmonic map q : B m → S m ℓ , m, ℓ ∈ N with ℓ ≤ m, which we recently constructed in [5] and thus deduce the existence of an explicit family of stable proper biharmonic maps to Euclidean spheres.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Navier-Stokes equation solutions
Geometry and complex manifolds
Publication details
- Journal / source
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- Publisher
- Scuola Normale Superiore - Edizioni della Normale
- Pages
- 14–14
- Publication date
- 7 April 2026
- Language
- EN