Infinite type germs of real analytic pseudoconvex domains in C3

In Lampert [On the boundary regularity of biholomorphic mappings, Contributions to several complex variables, Aspects Math. E9 (1986), pp. 193-215] and D'Angelo [Several Complex Variables and the Geometry of real Hypersurfaces, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993, ISBN: 0-8493-8272-6] Lempert and D'Angelo showed that germs of real analytic sets in C-n of infinite type contain a complex curve. In this article we discuss a very special case of their result, germs of real analytic pseudoconvex domains in C-3. We reprove their theorem using a geometric construction which sheds light on the intricate structure of such boundaries in the presence of complex curves of high order tangency. The proof of Lempert and D'Angelo is somewhat more of an ideal theoretic nature.