Antonio Ros and Rabah Souam

Abstract

Introduction. Consider a smooth and compact convex body B in R 3 . Let @B and int B denote its boundary and its interior respectively. We are interested in embedded constant mean curvature surfaces M in R 3 with non empty boundary such that int M ae int B and @M ae @B and which intersect @B at a constant angle fl 2 (0; ß). Such surfaces, called capillary surfaces, are critical points of an energy functional under some constraints. The energy functional is defined as follows: the surface M separates B into two bodies, consider among these two bodies the one inside which the angle fl is measured and call\Omega the part of its boundary that lies on @B. Denote by A<F59.5