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 ̃.

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