A note on relation between Azukawa izometries at one point and global biholomorphisms
Malgorzata Zajecka
TL;DR
This paper shows that under specific conditions, holomorphic functions that preserve Azukawa distances at a single point are actually biholomorphic mappings, revealing a strong link between local isometries and global automorphisms.
Contribution
It establishes a connection between local Azukawa isometries at one point and global biholomorphisms under certain assumptions, advancing understanding of complex geometric mappings.
Findings
Holomorphic functions that are Azukawa isometries at one point can be biholomorphisms.
Under certain assumptions, local isometries imply global biholomorphic equivalences.
The result bridges local distance-preserving properties with global complex structure transformations.
Abstract
We prove that under certain assumptions holomorphic functions which are Azukawa isometries at one point are in fact biholomorphisms.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Advanced Differential Equations and Dynamical Systems · Advanced Algebra and Geometry