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 ̃.

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