Extra extension properties of equidimensional holomorphic mappings: results and open questions
S. Ivashkovich
TL;DR
This paper reviews known extension properties of equidimensional holomorphic mappings, presents new results, and discusses open questions to guide future research in complex manifold mappings.
Contribution
It consolidates existing knowledge, introduces new findings, and proposes strategies and open questions for advancing the understanding of holomorphic mappings.
Findings
Known extension properties summarized
New results on extension properties proved
Open questions formulated for future research
Abstract
Holomorphic (nondegenerate) mappings between complex manifolds of the same dimension are of special interest. For example, they appear as coverings of complex manifolds. At the same time they have very strong "extra" extension properties in compare with mappings in different dimensions. The aim of this paper is to put together the known results on this subject, give some perspective on the general strategy for future progress, prove some new results and formulate open questions.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Geometric Analysis and Curvature Flows