Conformally invariant Monge-Ampère equations: Global solutions

Viaclovsky, Jeff

doi:10.1090/S0002-9947-00-02548-4

Conformally invariant Monge-Ampère equations: Global solutions
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by Jeff A. Viaclovsky PDF

Trans. Amer. Math. Soc. 352 (2000), 4371-4379 Request permission

Abstract:

In this paper we will examine a class of fully nonlinear partial differential equations which are invariant under the conformal group $SO(n+1,1)$. These equations are elliptic and variational. Using this structure and the conformal invariance, we will prove a global uniqueness theorem for solutions in $\mathbf {R}^n$ with a quadratic growth condition at infinity.

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