Multi-dimensional traveling fronts have been studied in the Allen-Cahn equation (Nagumo equation) and also in multistable reaction-diffusion equations recently. Two-dimensional V-form fronts are studied by Ninomiya and myself (2005) and also by Hamel, Monneau and Roquejoffre (2005). Rotationally symmetric traveling fronts are studied by several authors.In this talk I will give a brief survey on multi-dimensional traveling fronts, and explain what is different and what gives the difficulties compared with one-dimensional cases. Finally I explain recent works on three-dimensional traveling fronts of pyramidal shapes and those of convex polyhedral shapes.
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