On conformally invariant equations on \(\mathbf R^n\). (English) Zbl 1286.35076
Summary: In this paper we provide a complete characterization of fully nonlinear conformally invariant differential operators of any integer order on \(\mathbf R^n\), which extends the result proved for operators of the second order by A. Li and Y. Li [Commun. Pure Appl. Math. 56, No. 10, 1416–1464 (2003; Zbl 1155.35353)]. In particular we prove existence and uniqueness of a family of tensors (suitably invariant under Möbius transformations) which are the basic building blocks that appear in the definition of all conformally invariant differential operators on \(\mathbf R^n\). We also explicitly compute the tensors that are related to operators of order up to four.
MSC:
| 35G20 | Nonlinear higher-order PDEs |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
Citations:
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