Date of Graduation
8-2019
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor
Phillip Harrington
Committee Member
Andrew Raich
Second Committee Member
Ariel Barton
Abstract
Let Ω ⊂ Cn be a smooth, bounded, pseudoconvex domain, and let M ⊂ ∂Ω be a complex submanifold with rectifiable boundary. In 2017, Harrington studied the equation dM A = α ̃ on M, where α ̃ is D’Angelo’s 1-form and A is real. In this thesis, we will study a non-pseudoconvex example in which M has a non-rectifiable boundary. In spite of the lack of topological obstructions on the boundary, there are no continuous solutions to dM A = α ̃.
Citation
Humes, F. N. (2019). Smoothness of Defining Functions and the Diederich-Fornæss Index. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/3318