Conformally invariant differential equations and projective geometry
نویسندگان
چکیده
منابع مشابه
On certain conformally invariant systems of differential equations
Several systems of differential operators are constructed and their study is commenced. These systems are generalizations, in a reasonable sense, of the Heisenberg Laplacian operators introduced by Folland and Stein. In particular, they admit large groups of conformal symmetries; various real form of the special linear groups, even special orthogonal groups, and the exceptional group of type E6...
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There has been much work on conformally invariant fully nonlinear elliptic equations and applications to geometry and topology. See for instance [17], [5], [4], [10], [14], [9], and the references therein. An important issue in the study of such equations is to classify entire solutions which arise from rescaling blowing up solutions. Liouville type theorems for general conformally invariant fu...
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In this paper we provide a complete characterization of fully nonlinear conformally invariant differential operators of any integer order on R, which extends the result proved for operators of the second order by A. Li and the first named author in [38]. In particular we prove existence and uniqueness of a family of tensors (suitably invariant under Möbius transformations) which are the basic b...
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We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry. We will also present these results which include some Liouville type theorems, Harnack type inequalities, existence and compactness of solutions to some nonl...
متن کاملConformally invariant differential operators on tensor densities
Let Fλ be the space of tensor densities on R n of degree λ (or, equivalently, of conformal densities of degree −λn) considered as a module over the Lie algebra o(p+1, q+1). We classify o(p+1, q+1)-invariant bilinear differential operators from Fλ ⊗ Fμ to Fν . The classification of linear o(p + 1, q + 1)invariant differential operators from Fλ to Fμ already known in the literature (see [6, 9]) i...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1981
ISSN: 0022-1236
DOI: 10.1016/0022-1236(81)90002-1