Biharmonic map heat flow into manifolds of nonpositive curvature

By T. Lamm. 2004

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Conservation Laws for Fourth Order Systems in Four Dimensions (2006, background): “Global existence of solutions of the gradient flow for ℬ int has been shown by the first author (Lamm, 2005 ) in the case of a target manifold with non-positive sectional curvature.”
Biharmonic submanifolds of $${\mathbb{C}P^n}$$ (2009, background): “The analytic aspects of biharmonic maps as well as the differential geometry of such maps have been studied in the last decade (see, for example, [7, 17, 22, 23] and [2, 10, 16, 21, 24], respectively).”
A short survey on biharmonic maps between Riemannian manifolds (2005, background): “We shall not report on this aspect and we refer the reader to [33, 34, 53, 54, 55] and the references therein.”