Basic Properties

Serge Lang
Additional contact information
Serge Lang: Yale University, Department of Mathematics

Chapter Chapter I in Introduction to Complex Hyperbolic Spaces, 1987, pp 11-30 from Springer

Abstract: Abstract Kobayashi defined a natural semi distance on any complex space. Instead of linking two points by a chain of real curves and taking their lengths and inf via a hermitian or Riemannian metric, he joins points by a chain of discs and takes the inf over the hyperbolic metric. He calls a complex space hyperbolic when the semi distance is a distance. We shall describe the basic properties of such spaces. The most fundamental one is that a holomorphic map is distance decreasing, and hence that a family of holomorphic maps locally is equicontinuous. This gives the possibility of applying Ascoli’s theorem for families of such maps. Such an application has wide ramifications, including possible applications to problems associated with Mordell’s conjecture (Faltings’ theorem) and possible generalizations.

Keywords: Distance Function; Complex Space; Semi Distance; Hyperbolic Distance; Complex Subspace (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-1945-1_2

Ordering information: This item can be ordered from
http://www.springer.com/9781475719451

DOI: 10.1007/978-1-4757-1945-1_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().