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COMPLEX CURVES IN ALMOST-COMPLEX

MANIFOLDS AND MEROMORPHIC HULLS

Sergei IVASHKOVICH – Vsevolod SHEVCHISHIN

[**Preface**]{}

[Chapter I. Local Properties of Complex Curves.]{}

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[Chapter II. Compactness Theorem.]{}

[**Lecture 10. Envelopes of Meromorphy of Two-Spheres. pp. 160–168**]{}

[**Appendix IV. Complex Points and Stein Neighborhods. pp. 169–172**]{}

[**Appendix V. Seiberg-Witten Invariants and Envelopes. pp. 173–181**]{}

[**References. pp. 182–186**]{}

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**P r e f a c e**

This are the notes of a course, given by the first author for the Graduiertenkollegs (= graduate students) at the Ruhr-University of Bochum, in December, 1997. Previously, shorter courses were given in Göteborg, Warsaw and Bonn.

These lectures pursued two main tasks:

[**First**]{} — to give a systematic and self-contained introduction to the Gromov theory of so-called pseudoholomorphic curves (a term which will be completely eliminated in these notes). This is handled in Chapters I,II,III.

[**Second**]{} — to explain our joint results on envelopes of meromorphy of real two-spheres in complex two-dimensional manifolds, which we obtained using Gromov theory. We do this in Chapter IV.

It was impossible, of course, to omit the original motivation of Gromov in the development of the subject:

- in Appendix III, §A3.5, we 