Rotationally symmetric hypersurfaces with prescribed mean curvature

Marie-Françoise Bidaut-Véron

Vol. 173 (1996), No. 1, 29–67

DOI: 10.2140/pjm.1996.173.29

Abstract

Here we study the singular radial solutions of the prescribed mean curvature equation

where f is increasing and has the sign of u near infinity. We prove the local existence of a generalized singular solution under slight growth assumptions on f. In the physical case N = 2 we prove that the curve is asymptotic to the curve r|f(u)| = 1. We also study the global behaviour of the solutions.

Mathematical Subject Classification 2000

Primary: 58E15

Secondary: 35J60, 53A10

Milestones

Received: 20 July 1993

Revised: 10 December 1993

Published: 1 March 1996