Complex tangential flows and compactness of the $\bar{\partial}$- Neumann operator

Samangi Munasinghe; Emil J. Straube

Complex tangential flows and compactness of the $\bar{\partial}$- Neumann operator

Complex Variables 2007-05-23 v1 Analysis of PDEs

Authors: Samangi Munasinghe , Emil J. Straube

Abstract

We provide geometric conditions on the set of boundary points of infinite type of a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$ which imply that the $\bar{\partial}$ -Neumann operator is compact. These conditions are formulated in terms of certain short time flows in suitable complex tangential directions. It is noteworthy that compactness is \emph{not} established via the known potential theoretic sufficient conditions. Our results generalize to $\mathbb{C}^{n}$ the corresponding $\mathbb C^{2}$ results due to the second author.

Keywords

pseudoconvex domains geodesic flow geometric flows

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@article{arxiv.math/0607685,
  title  = {Complex tangential flows and compactness of the $\bar{\partial}$- Neumann operator},
  author = {Samangi Munasinghe and Emil J. Straube},
  journal= {arXiv preprint arXiv:math/0607685},
  year   = {2007}
}

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9 pages

Complex tangential flows and compactness of the $\bar{\partial}$- Neumann operator

Abstract

Keywords

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