Existence of a somewhere injective pseudo-holomorphic disc

2000 ◽  
Vol 10 (4) ◽  
pp. 829-862 ◽  
Author(s):  
L. Lazzarini
Keyword(s):  
Holomorphic Disc

Neighborhood of an Embedded J-Holomorphic Disc

2009 ◽  
Vol 20 (1) ◽  
pp. 168-176 ◽  
Author(s):  
Uroš Kuzman
Keyword(s):  
Holomorphic Disc

scholarly journals Seidel elements and potential functions of holomorphic disc counting

2017 ◽  
Vol 69 (3) ◽  
pp. 327-368 ◽  
Author(s):  
Eduardo González ◽  
Hiroshi Iritani
Keyword(s):  
Potential Functions ◽  
Holomorphic Disc ◽  
Seidel Elements

scholarly journals Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps

2017 ◽  
Vol 28 (04) ◽  
pp. 1750028 ◽  
Author(s):  
Yuta Kusakabe
Keyword(s):  
Complex Manifold ◽  
Convex Domain ◽  
Holomorphic Curves ◽  
Holomorphic Maps ◽  
Stein Space ◽  
Bounded Convex Domain ◽  
Path Component ◽  
Oka Manifold ◽  
Holomorphic Disc ◽  
Bounded Convex

We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain [Formula: see text] and any connected complex manifold [Formula: see text], the space [Formula: see text] contains a dense holomorphic disc. Our second result states that [Formula: see text] is an Oka manifold if and only if for any Stein space [Formula: see text] there exists a dense entire curve in every path component of [Formula: see text]. In the second half of this paper, we apply the above results to the theory of universal functions. It is proved that for any bounded convex domain [Formula: see text], any fixed-point-free automorphism of [Formula: see text] and any connected complex manifold [Formula: see text], there exists a universal map [Formula: see text]. We also characterize Oka manifolds by the existence of universal maps.

Sign in / Sign up

Export Citation Format

Share Document