Date of Graduation
8-2019
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
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