Relative Equilibria in the 4-Vortex Problem Bifurcating from an Equilateral Triangle Configuration

We study the relative equilibria in the 4-vortex problem when two of vorticities are equal to 1, and the other two equal to m are enough small. We prove that for m > 0 there is a unique concave kite relative equilibria. We also prove that there is a unique convex planar relative equilibria having two pairs of equal vorticities located at the adjacent vertices of the configuration and it is an isosceles trapezoid.