Convergence properties of the Gronwall area formula for quadratic Julia   sets
  Using parabolic enrichment, it is shown that Gronwall area formula for the filled Julia set along the boundary of the main cardioid of the Mandelbrot set cannot be well approximated by replacing it by a finite sum.   A revised version of this article will appear in the Journal of the London Mathematical Society. 
Alexandre Dezotti
math.DS math.CV