The Hull of a Curve in C n

Problème du bord dans l'espace projectif complexe

“…Pour p = 1, ce problème du bord est très lié à l'étude des enveloppes polynomiales et des mesures orthogonales publiée dans plusieurs articles comme [24], [25], [2], [23], [l], [19], [5], [6], [20]. Les résultats de ces travaux sont utilisés pour la résolution du problème du bord avec p > 1 [4], [5].…”

On the polynomial moment problem

“…The case when δ is an image of S 1 under the map z → (f (z), g(z)), where f (z), g(z) are functions analytic in an annulus containing S 1 was investigated earlier by J. Wermer [12]: in this case the moment condition is equivalent to the condition that there exists a finite Riemann surface Σ with border S 1 such that f (z), g(z) have an analytic extension to Σ.…”

Polynomial hulls and positive currents

“…The first result in this direction is due to Wermer [37], who proved that if Γ is a real analytic curve, then Γ \ Γ is subvariety (possibly empty) of C n \ Γ. Using a tool developed by Bishop [10], Stolzenberg [35] was able to extend Wermer's theorem to the C 1 case; Alexander [4] extended it to the case where Γ is connected.…”