Characterization of convex domains in ℂ2 with non-compact automorphism group View Full Text


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Article Info

DATE

2017-03-30

AUTHORS

Kaylee Hamann, Bun Wong

ABSTRACT

In the field of several complex variables, the Greene-Krantz Conjecture, whose consequences would be far reaching, has yet to be proven. The conjecture is as follows: Let D be a smoothly bounded domain in ℂn. Suppose there exists {gj} ⊂ Aut(D) such that {gj(z)} accumulates at a boundary point p ∈ ∂D for some z ∈ D. Then ∂D is of finite type at p. In this paper, we prove the following result, yielding further evidence to the probable veracity of this important conjecture: Let D be a bounded convex domain in ℂ2 with C2 boundary. Suppose that there is a sequence {gj} ⊂ Aut(D) such that {gj(z)} accumulates at a boundary point for some point z ∈ D. Then if p ∈ ∂D is such an orbit accumulation point, ∂D contains no non-trivial analytic variety passing through p. More... »

PAGES

977-984

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11425-016-9031-6

DOI

http://dx.doi.org/10.1007/s11425-016-9031-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1084031481


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