TY - JOUR
T1 - Characterizations of boundaries of holomorphic 1-chains within ℂ ̂ × ℂ̂ and ℂ ̂ × ℂ̂
AU - Walker, Ronald A.
N1 - Funding Information:
This work is based in part on work supported by a NSF Graduate Fellowship while the author was at the University of Michigan and work while the author was a VIGRE Ross Assistant Professor at the Ohio State University.
PY - 2008/10
Y1 - 2008/10
N2 - By way of a particular Cauchy-type integral, we characterize the closed rectifiable 1-currents γ, with support contained in ℂ 2 and satisfying condition A 1, that bound holomorphic 1-chains within ℂ̂× ℂ̂ . Also, we derive characterizations for the boundaries of holomorphic 1-chains within ℂ̂× ℂ̂, which yield examples of characterizations within a non-compact, non-Stein space. Additionally, we illustrate a connection between some of these characterizations and the Cauchy integral characterization of boundary values of meromorphic and holomorphic functions over a domain in ℂ.
AB - By way of a particular Cauchy-type integral, we characterize the closed rectifiable 1-currents γ, with support contained in ℂ 2 and satisfying condition A 1, that bound holomorphic 1-chains within ℂ̂× ℂ̂ . Also, we derive characterizations for the boundaries of holomorphic 1-chains within ℂ̂× ℂ̂, which yield examples of characterizations within a non-compact, non-Stein space. Additionally, we illustrate a connection between some of these characterizations and the Cauchy integral characterization of boundary values of meromorphic and holomorphic functions over a domain in ℂ.
UR - http://www.scopus.com/inward/record.url?scp=84868003865&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84868003865&partnerID=8YFLogxK
U2 - 10.1007/s12220-008-9036-9
DO - 10.1007/s12220-008-9036-9
M3 - Article
AN - SCOPUS:84868003865
SN - 1050-6926
VL - 18
SP - 1159
EP - 1170
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 4
ER -