This paper studies the constant mean curvature surface in asymptotically flat 3-manifolds with general asymptotics. Under some weak conditions, the foliation of stable spheres of constant mean curvature is shown to be unique outside some compact set in the asymptotically flat 3-manifold with positive mass.

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In this paper we study asymptotic behavior of n-superharmonic functions at isolated singularity using the Wolff potential and n-capacity estimates in nonlinear potential theory. Our results are inspired by and extend [AH73] of Arsove-Huber and [Tal06] of Taliaferro in 2 dimensions. To study n-superharmonic functions we use a new notion of thinness by n-capacity motivated by a type of Wiener criterion in [AH73]. To extend [Tal06], we employ the Adams-Moser-Trudinger inequality for the Wolff potential, which is inspired by the one used in [BM91] of Brezis-Merle (cf. [Io09]). For geometric applications, we study the asymptotic end behavior of complete conformally flat manifolds as well as complete properly embedded hypersurfaces in hyperbolic space, both with nonnegative Ricci curvature. These geometric applications seem to elevate the importance of n-Laplace equations and make a closer tie to the classic analysis developed in conformal geometry in general dimensions.

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