Geometry of the triple junction between three fluids in equilibrium

Abstract

We present an approach to the problem of the blow up at the triple junction of three uids in equilibrium. Although many of our results can already be found in the literature, our approach is almost self-contained and uses the theory of sets of nite perimeter without making use of more advanced topics within geometric measure theory. Specically, using only the calculus of variations we prove two monotonicity formulas at the triple junction for the three-uid conguration, and show that blow up limits exist and are always cones. We discuss some of the geometric consequences of our results.