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| From "Math for Poets..." |
Mathew Gluck
The Method of Moving Spheres
Abstract. The method of moving spheres is a powerful and versatile method for analyzing partial differential equations with conformal symmetry. At the core of this method is the amazing fact that one can classify all suitably nice functions f defined on Euclidean space for which both of the following properties hold:
1. For all points x there is a sphere centered at x about which f has inversion symmetry, and
2. for all directions e, there is a hyperplane with normal direction e about which f has reflection symmetry.
I will give some examples of functions for which both properties hold, and I will discuss the historical development of the classification of all such functions. Finally, I will overview the method of moving spheres and provide some applications of the method in the analysis of conformally covariant partial differential equations.
