POLYNOMIAL CONVEXITY

By PAUL WHITE

CONTENTS INTRODUCTION POLYNOMIAL CONVEXITY UNIFORM ALGEBRAS PLURISUBHARMONIC FUNCTIONS THE CAUCHY–FANTAPPIÈ INTEGRAL THE OKA–WEIL THEOREM SOME EXAMPLES HULLS WITH NO ANALYTIC STRUCTURE SOME GENERAL PROPERTIES OF POLYNOMIALLY CONVEX SETS APPLICATIONS OF THE COUSIN PROBLEMS TWO CHARACTERIZATIONS OF POLYNOMIALLY CONVEX SETS APPLICATIONS OF MORSE THEORY AND ALGEBRAIC TOPOLOGY CONVEXITY IN STEIN MANIFOLDS SETS OF FINITE LENGTH INTRODUCTION ONE-DIMENSIONAL VARIETIES GEOMETRIC PRELIMINARIES FUNCTION-THEORETIC PRELIMINARIES SUBHARMONICITY RESULTS ANALYTIC STRUCTURE IN HULLS FINITE AREA THE CONTINUATION OF VARIETIES INTRODUCTORY REMARKS MEASURE-THEORETIC PRELIMINARIES SETS OF CLASS A1 STOKES’S THEOREM THE MULTIPLICITY FUNCTION COUNTING THE BRANCHES FURTHER RESULTS ISOPERIMETRY REMOVABLE SINGULARITIES SURFACES IN STRICTLY PSEUDOCONVEX BOUNDARIES APPROXIMATION TOTALLY REAL MANIFOLDS HOLOMORPHICALLY CONVEX SETS APPROXIMATION ON TOTALLY REAL MANIFOLDS SOME TOOLS FROM RATIONAL APPROXIMATION ALGEBRAS ON SURFACES TANGENTIAL APPROXIMATION VARIETIES IN STRICTLY PSEUDOCONVEX DOMAINS INTERPOLATION BOUNDARY REGULARITY UNIQUENESS EXAMPLES AND COUNTEREXAMPLES UNIONS OF PLANES AND BALLS PLURIPOLAR GRAPHS DEFORMATIONS SETS WITH SYMMETRY REFERENCES