Abstract
Steady state dendritic growth at zero surface tension is analysed both in two-dimensional and three-dimensional geometries. It is demonstrated that the solutions found by Ivantsov (1947) and later extended by Horvay and Cahn (1961) are obtained under very general assumptions. In two-dimensional growth, Ivantsov's ansatz is equivalent to searching for solutions in the space of conformal transformations. We show that the parabolae are the unique solutions in this space. For the three-dimensional dendrite problem, we rederive, by a new method, the previously found solutions and prove that they are the only ones allowed by Ivantsov's ansatz. Finally, the linearization around Ivantsov's paraboloid is given in a more convenient form.