On Some Conformally Invariant Fully Nonlinear Equations

Conformally 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 .

A Liouville type theorem for some conformally invariant fully nonlinear equations

Following the approach in our earlier paper [2] and using the gradient estimates developed in [2] and [3], we give another Liouville type theorem for some conformally invariant fully nonlinear equations. Various Liouville type theorems for conformally invariant equations have been obtained by Obata, Gidas-Ni-Nirenberg, CaffarelliGidas-Spruck, Viaclovsky, Chang-Gursky-Yang, and Li-Li. For these,...

Further results on Liouville type theorems for some conformally invariant fully nonlinear equations

A general Liouville type theorem for some conformally invariant fully nonlinear equations

Various Liouville type theorems for conformally invariant equations have been obtained by Obata ([9]), Gidas, Ni and Nirenberg ([4]), Caffarelli, Gidas and Spruck ([1]), Viaclovsky ([10] and [11]), Chang, Gursky and Yang ([2] and [3]), and Li and Li ([5], [6] and [7]). See e. g. theorem 1.3 and remark 1.6 in [6] where these results (except for the one in [7]) are stated more precisely. In this ...

Degenerate 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...