Some envelopes of holomorphy

A Schlichtness Theorem for Envelopes of Holomorphy

Let Ω be a domain in C. We prove the following theorem. If the envelope of holomorphy of Ω is schlicht over Ω, then the envelope is in fact schlicht. We provide examples showing that the conclusion of the theorem does not hold in Cn, n > 2. Additionally, we show that the theorem cannot be generalized to provide information about domains in C whose envelopes are multiply sheeted.

Some explorations in holomorphy.

In supersymmetric theories, one can obtain striking results and insights by exploiting the fact that the superpotential and the gauge coupling function are holomorphic functions of the model parameters. The precise meaning of this holomorphy is subtle, and has been explained most clearly by Shifman and Vainshtein, who have stressed the role of the Wilsonian eeective action. In this note, we ela...

Envelopes of Holomorphy and Extension of Functions of Bounded Type

In this article we characterize the envelope of holomorphy for the algebra of bounded type holomorphic functions on Riemann domains over a Banach space in terms of the spectrum of the algebra. We prove that evaluations at points of the envelope are always continuous but we show an example of a balanced open subset of c0 where the extensions to the envelope are not necessarily of bounded type, a...

On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle

Analytic Continuation , Envelopes of Holomorphy , and Projective and Direct Limit Spaces

For a Riemann domain Í2, a connected complex manifold where n (n = dimension) globally defined functions form a local system of coordinates at every point, and an arbitrary holomorphic function / in Í2, the "Riemann surface" Slf, a maximal holomorphic extension Riemann domain for /, is formed from the direct limit of a sequence of Riemann domains. Projective limits are used to construct an enve...