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A Scalar Associated with the Inverse of Some Abelian Integrals and a Ramified Riemann Domain
[article]
2015
arXiv
pre-print
We introduce a positive scalar function ρ(a, Ω) for a domain Ω of a complex manifold X with a global holomorphic frame of the cotangent bundle by closed Abelian differentials, which heuristically measure the distance from a ∈Ω to the boundary Ω. We prove an estimate of Cartan--Thullen type with ρ(a, Ω) for holomorphically convex hulls of compact subsets. In one dimensional case, we apply the obtained estimate of ρ(a, Ω) to give a new proof of Behnke-Stein's Theorem for the Steiness of open
arXiv:1502.01548v2
fatcat:i2c5ngvo2fh4ln6undsmewqcva