Vol. 234, No. 1, 2008

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Convexity in locally conformally flat manifolds with boundary

Marcos Petrúcio de A. Cavalcante

Vol. 234 (2008), No. 1, 23–31
Abstract

Given a closed subset Λ of the open unit ball B1 n for n 3, we consider a complete Riemannian metric g on B 1 Λ of constant scalar curvature equal to n(n 1) and conformally related to the Euclidean metric. We prove that every closed Euclidean ball B B1 Λ is convex with respect to the metric g, assuming the mean curvature of the boundary ∂B1 is nonnegative with respect to the inward normal.

Keywords
scalar curvature, locally conformally flat metric, convexity
Mathematical Subject Classification 2000
Primary: 53A30, 53C21
Secondary: 52A20
Milestones
Received: 19 January 2007
Revised: 8 June 2007
Accepted: 5 September 2007
Published: 1 January 2008
Authors
Marcos Petrúcio de A. Cavalcante
Instituto de Matemática
Universidade Federal de Alagoas
Campus A. C. Simões, BR 104 Norte, Km 97
57072-970 Maceió, AL
Brazil