Modifications of the Levi core

John (Nick) Treuer (UC San Diego)

Nov 22. 2023, 10:00 — 10:50

In 2021, Dall'Ara and Mongodi introduced the Levi core $\mathfrak{C}(\mathcal{N})$, a subdistribution of the Levi null space, and showed that it could be used to study regularity properties of the $\overline{\partial}$-Neumann operator. In 2022, the speaker showed that if the support of the Levi core satisfies Property ($P$), then the boundary of the domain satisfies Property ($P$).  He also gave an example of a Hartogs domain in $\mathbb{C}^2$ which satisfies Property ($P$) yet the support of the Levi core was large in a measure-theoretic sense.    In this talk, we modify the algorithm for constructing the Levi core to give a new modified core $\mathcal{M}\mathfrak{C}$.  This new core is a subdistribution of the Levi core $\mathfrak{C}(\mathcal{N})$.  We examine properties of the modified Levi core in relation to the regularity of the $\overline{\partial}$-Neumann operator and revisit the Hartogs domain example. This is joint work with Tanuj Gupta (Texas A\&M University) and Emil Straube (Texas A\&M University).

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Analysis and Geometry in Several Complex Variables (Workshop)
Peter Ebenfelt (UC San Diego)
Purvi Gupta (IIS Bengalore)
Bernhard Lamel (U of Vienna)
Nordine Mir (Texas A&M U at Qatar)