On the asymptotic behaviour of capillary surfaces in cusps

Abstract

Concus and Finn [2] discovered that capillary surfaces rise to infinity in corners with sufficiently small opening angle. They also found the leading term of an asymptotic expansion. Miersemann [5] improved this result to obtain a complete asymptotic expansion. In the present paper we will apply the methods of the above authors to discuss asymptotic behaviour of capillarities in cusps, which is a corner with opening angle 0. A large variety of asymptotic formulas will be provided. The general comparison theorem from Concus and Finn will play an important role in the proofs.