Abstract

Abstract:

In this paper we establish two boundary versions of the Schwarz lemma. The first is for general holomorphic self maps of bounded convex domains with $C^2$ boundary. This appears to be the first boundary Schwarz lemma for general holomorphic self maps that requires no strong pseudoconvexity or finite type assumptions. The second is for biholomorphisms of domains who have an invariant K{\"a}hler metric with bounded sectional curvature. This second result applies to holomorphic homogeneous regular domains and appears to be the first boundary Schwarz lemma that makes no assumptions on the regularity of the boundary.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 119-168
Launched on MUSE
2022-01-13
Open Access
No
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