67 research outputs found
Extremal discs and the holomorphic extension from convex hypersurfaces
Let D be a convex domain with smooth boundary in complex space and let f be a
continuous function on the boundary of D. Suppose that f holomorphically
extends to the extremal discs tangent to a convex subdomain of D. We prove that
f holomorphically extends to D. The result partially answers a conjecture by
Globevnik and Stout of 1991
Holomorphic embeddings of planar domains into C 2
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46245/1/208_2005_Article_BF01461006.pd
Holomorphic functions on rotation invariant families of curves passing through the origin
Boundary functions on a bounded balanced domain
summary:We solve the following Dirichlet problem on the bounded balanced domain with some additional properties: For and a positive lower semi-continuous function on with for , we construct a holomorphic function such that for , where
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