ON CONFORMALLY INVARIANT EQUATIONS ON Rn
نویسندگان
چکیده
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 building blocks that appear in the definition of all conformally invariant differential operators on R. We also explicitly compute the tensors that are related to operators of order up to four.
منابع مشابه
On Isometric and Conformal Rigidity of Submanifolds
Let f, g : Mn → Rn+d be two immersions of an n-dimensional differentiable manifold into Euclidean space. That g is conformal (isometric) to f means that the metrics induced on Mn by f and g are conformal (isometric). We say that f is conformally (isometrically) rigid if given any other conformal (isometric) immersion g there exists a conformal (isometric) diffeomorphism Υ from an open subset of...
متن کاملOn Positive Solutions to Semi-linear Conformally Invariant Equations on Locally Conformally Flat Manifolds
In this paper we study the existence and compactness of positive solutions to a family of conformally invariant equations on closed locally conformally flat manifolds. The family of conformally covariant operators Pα were introduced via the scattering theory for Poincaré metrics associated with a conformal manifold (Mn, [g]). We prove that, on a closed and locally conformally flat manifold with...
متن کاملConformally invariant fully nonlinear elliptic equations and isolated singularities
1 Introduction There has been much work on conformally invariant fully nonlinear elliptic equations and applications to geometry and topology. [10], and the references therein. In this and a companion paper [16] we address some analytical issues concerning these equations. For n ≥ 3, consider −∆u = n − 2 2 u n+2 n−2 , on R n .
متن کاملOn the Local Smoothing for a Class of Conformally Invariant Schrödinger Equations
We present some a-priori bounds from above and from below for solutions to a class of conformally invariant Schrödinger equations. As a by-product we deduce some new uniqueness results.
متن کاملDegenerate Conformally Invariant Fully Nonlinear Elliptic Equations
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011