Isoperimetric Sandwiches and Approximation by Analytic and Harmonic Functions

Catherine Bénéteau is an Associate Professor at the University of South Florida. She has secured numerous grants and awards for her work, and organised many conferences and workshops. She is a Referee for several top journals including Complex Analysis and Operator Theory, Complex Variables and Elliptic Equations, Computational Methods and Function Theory. Dmitry Khavinson is a Distinguished University Professor, University of South Florida. With a long history of high quality publications in this area, he is an established authority in this field. He has been awarded numerous grants and awards for his work including the 2015 USF Outstanding Faculty Achievement Award.

Introduction. Analytic content in Smirnov and Bergman norms. Toeplitz operators, isoperimetric inequalities, Bergman orthogonal polynomials. Higher dimensions: harmonic approximation and isoperimetric inequalities. Other free boundary problems in two dimensions. Concluding Remarks