Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Polynomial Density Of Compact Smooth Surfaces, Luke P. Broemeling
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
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..