Uniqueness Theorems for fully nonlinear conformal equations on subdomains of the sphere

2015/05/04 by Cavalcante, Marcos P., Espinar, José M.
#58Jxx #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53Cxx #Secondary 35Pxx

paper · doi:10.48550/arxiv.1505.00733

Abstract

In this paper we prove classification results to elliptic fully nonlinear conformal equations on certain subdomains of the sphere with prescribed constant mean curvature on its boundary. Such subdomains are the hemisphere (or a geodesic ball on \mathbbSⁿ) of dimension n≥ 2 with prescribed constant mean curvature on its boundary, and annular domains with minimal boundary. Our results extend the classifications of Escobar in \citeE0 when n≥ 3, and Hang-Wang in \citeHaWa and Jimenez in \citeJ when n=2.

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