Differential Geometry Seminar - Christine Breiner

Abstract: Critical points for the functional $E(u)= \int |\Delta u|^2$ are called biharmonic maps and are natural fourth order analogues of harmonic maps. Compactness theory for harmonic maps in two dimensions is well understood. In this talk we will discuss work with T. Lamm in which we determine the full compactness theory for sequence of approximate biharmonic maps from four dimensional manifolds into spheres. In particular, we prove small energy compactness, energy quantization and the "no neck" property. We discuss how we exploit the structure of the Euler-Lagrange equation to conclude the result, even when the inhomogeneous term is in L log L.