Testing holomorphy on curves

2010/12/20 by Fridman, Buma L., Ma, Daowei
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1012.4329

Abstract

For a domain D⊂ ℂⁿ we construct a continuous foliation of D into one real dimensional curves such that any function f∈ C¹(D) which can be extended holomorphically into some neighborhood of each curve in the foliation will be holomorphic on D.

Related

• Holomorphic functions on subsets of C
• About C^∞ foliations by holomorphic curves on complex surfaces
• Wild boundary behaviour of holomorphic functions in domains of ℂ^N
• On a neighborhood of a torus leaf of a certain class of holomorphic foliations on complex surfaces
• Leafwise Holomorphic Functions