Date of Graduation
Doctor of Philosophy in Mathematics (PhD)
Second Committee Member
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 ̃.
Humes, Felita Nadia, "Smoothness of Defining Functions and the Diederich-Fornæss Index" (2019). Theses and Dissertations. 3318.