Special power series expansions of monogenic functions around surfaces of codimension two

In this paper we will focus on power series expansions around special surfaces of codimension two, in particular around spheres and products of spheres. This will include a version of the Cauchy–Kowalewski extension theorem around these surfaces. This higher codimension result was only obtained so far in the flat case (see Partial Differential Equations with Complex Analysis. Pitman Research Notes Mathematical Series, vol. 262. Longman Science and Technology: Harlow, 1992; 61–92; Mathematics and its Applications, vol. 53. Kluwer Academic Publishers Group: Dordrecht, 1992). Copyright © 2008 John Wiley & Sons, Ltd.