Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Theses/Dissertations

Mathematics

Electronic Thesis and Dissertation Repository

Polynomial convexity

Publication Year

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Polynomial Density Of Compact Smooth Surfaces, Luke P. Broemeling Jul 2023

Polynomial Density Of Compact Smooth Surfaces, Luke P. Broemeling

Electronic Thesis and Dissertation Repository

We show that any smooth closed surface has polynomial density 3 and that any connected compact smooth surface with boundary has polynomial density 2.


Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, Octavian Mitrea Aug 2019

Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, Octavian Mitrea

Electronic Thesis and Dissertation Repository

The goal of this dissertation is to prove two results which are essentially independent, but which do connect to each other via their direct applications to approximation theory, symplectic geometry, topology and Banach algebras. First we show that every smooth totally real compact surface in complex Euclidean space of dimension 2 with finitely many isolated singular points of the open Whitney umbrella type is locally polynomially convex. The second result is a characterization of the rational convexity of a general class of totally real compact immersions in complex Euclidean space of dimension n..