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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
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About principal values and Wirtinger derivative
Let $K$ be a compact of the plane of Lebesgues measure 0 and $\Omega$ a domain containing $K$. Denote by $E$ the vector space of functions that are holomorphic on $\Omega - K$.
I'm interested in kno …
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Caratheodory's theorem in any compact Riemann surface
The classical Caratheodory theorem states that if $G$ is a simply connected domain in the plane, whose boundary is a Jordan curve, then the Riemann uniformization extends continuously to a homeomorphi …