Quasiconformality of pseudo-conformal transformations and deformations of hypersurfaces in C...
A quasiharmonic field is a pair of vector fields satisfying , , and coupled by a distorsion inequality. For a given , we construct a matrix field such that . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
We give a sufficient condition for a hermitian holomorphic vector bundle over the disk to be quasi-isometric to the trivial bundle. One consequence is a version of Cartan's lemma on the factorization of matrices with uniform bounds.