Biharmonic maps from R4 into a Riemannian manifold

By Changyou Wang. 2004

129 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/13c3fa775d7b3717c68b67023b5eff9cf6c1d698

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Biharmonic maps and morphisms from conformal mappings (2008, background): “(ii) An alternative to E2 is to view (N, h) isometrically immersed in RN and, considering φ as a vector, take the L2-norm of φ and call the critical points (extrinsic) biharmonic maps.”
Remarks on biharmonic maps into spheres (2004, methodology): “Among other things, there are two key ingredients in [ W1 , 2]. The first is the construction of an optimal (or Coulomb gauge) frame fields along the biharmonic maps, which was motivated by that of Yang-Mills fields by Uhlenbeck [U1,2] for m =4 and by Meyer-Rivi´ ere [MR] for m ≥ 5. The second is to”
Regularity of n/2-harmonic maps into spheres (2010, unknown): “Wang [Wan04] and C.”
Biharmonic map heat flow into manifolds of nonpositive curvature (2004, methodology): “This is done by inverting R 4 at S 3 ((1.4) is invariant under this inversion) and using the regularity result of C. Wang [ 19 ].”
Regularity of polyharmonic maps in the critical dimension (2009, methodology): “For higher domain dimension, a variant of Wang’s biharmonic proof [24] should be expected to apply.”
A short survey on biharmonic maps between Riemannian manifolds (2005, background): “e is the analytic aspect from the point of view of PDE: biharmonic maps are solutions of a fourth order strongly elliptic semilinear PDE. We shall not report on this aspect and we refer the reader to [33, 34, 53, 54, 55] and the references therein. The diﬀerential geometric aspect of biharmonic subm”
On biharmonic maps and their generalizations (2003, unknown): “Wang obtained, in a series of recent preprints [35], [ 36 ] and [37], another new proof of Theorem 1.1 and of Proposition 2.1.”
Conservation Laws for Fourth Order Systems in Four Dimensions (2006, methodology): “The regularity of solutions of special cases of (1.12) was first studied by Wang (2004a).”