申論題

(3) ([30%]) Consider a regular surface S where and the inversion Φ :R^3＼  given by

Compare the mean curvature and the Gauss urvatures of S and of the image surface S' = Φ(S). More precisely, show that and where N(p) is the unit normal of S at p, H'(Φ(p) is the mean curvature of s' at Φ(p), K'(Φ(p) is the Gauss curvature of S' at Φ(p).