Abstract
In this chapter, we will be concerned with the space of J-holomorphic maps of compact Riemann surfaces (S, J s ) into a fixed compact almost complex manifold (V, J). Even if an upper bound on area is imposed, this space is not compact in general.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
E. Bishop, Conditions for the analyticity of certain sets, Michigan Math. J. 11 (1964), 289–304.
J.P. Bourguignon, Analytical problems arising in geometry: examples from Yang-Mills theory, Jber. Dt. Math. Verein. 87 (1985), 67–89.
M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Inventiones Math. 82 (1985), 307–347.
D. Mumford, A remark on Mahler’s compactness theorem, Proc. Amer. Math. Soc. 28 (1971), 289–294.
T. Parker, J. Wolfson, Pseudoholomorphic mmaps and bubble trees, The Journal of Geom. Analysis 3 (1993), 63–98.
J. Sacks, K. Uhlenbeck, The existence of minimal immersions of two spheres, Ann. of Math. 113 (1981), 1–24.
Rugang Ye, Gromov’s compactness theorem for pseudoholomorphic curves, Preprint Univ. Cal. Santa Barbara (1991).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Basel AG
About this chapter
Cite this chapter
Pansu, P. (1994). Compactness. In: Audin, M., Lafontaine, J. (eds) Holomorphic Curves in Symplectic Geometry. Progress in Mathematics, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8508-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8508-9_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9656-6
Online ISBN: 978-3-0348-8508-9
eBook Packages: Springer Book Archive