Hardy–Sobolev extremals, hyperbolic symmetry and scalar curvature equations

a b s t r a c t Article history: Received 16 April 2008 Revised 5 September 2008 Available online 22 October 2008 MSC: primary 35J60 secondary 35B05, 35A15 We prove nondegeneracy of extremals for some Hardy–Sobolev– Maz’ya inequalities and present applications to scalar curvaturetype problems, including the Webster scalar curvature equation in a cylindrically symmetric setting. The main theme is hyperbolic symmetry. © 2008 Elsevier Inc. All rights reserved.