Remarks on biharmonic maps into spheres

On biharmonic maps and their generalizations

Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove t...

Compactness Results for Sequences of Approximate Biharmonic Maps

In this article, we prove energy quantization for approximate (intrinsic and extrinsic) biharmonic maps into spheres where the approximate map is in L logL. Moreover, we demonstrate that if the L logL norm of the approximate maps does not concentrate, the image of the bubbles are connected without necks.

Remarks on biharmoni maps into spheres

A Regularity Theory of Biharmonic Maps

In this article we prove the regularity of weakly biharmonic maps of domains in Euclidean four space into spheres, as well as the corresponding partial regularity result of stationary biharmonic maps of higher-dimensional domains into spheres. c © 1999 John Wiley & Sons, Inc. Introduction In this article we consider the notion of biharmonic maps and begin an analytic study of the regularity pro...

Stability of F-biharmonic maps

This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.