Let (M, g) be a four dimensional compact Riemannian manifold without boundary, (N, h) ⊂ R be a compact Riemannian submanifold without boundary. We establish the existence of a global weak solution to the heat flow of extrinsic biharmonic maps from M to N , which is smooth away from finitely many singular times. As a consequence, we prove that if Π4(N) = {0}, then any free homotopy class α ∈ [M,...

In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for generalized stable maps.

The object of the present paper was to study biharmonic maps on f-Kenmotsu manifolds and with Schouten–van Kampen connection. With help this connection, our results provided important insights related harmonic 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.