Hausdorff-$(2n-2)$ dimensional measure zero set and compactness of the $\overline{\partial}$-Neumann operator on $(0,n-1)$ forms

Yue Zhang

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arXiv · 1903.04112

Hausdorff-$(2n-2)$ dimensional measure zero set and compactness of the $\overline{\partial}$-Neumann operator on $(0,n-1)$ forms

Yue Zhang

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Abstract

By using a variant Property $(P_q)$ of Catlin, we discuss the relation of small set of weakly pseudoconvex points on the boundary of pseudoconvex domain and compactness of the $\overline{\partial}$-Neumann operator. In particular, we show that if the Hausdorff $(2n-2)$-dimensional measure of the weakly pseudoconvex points on the boundary of a smooth bounded pseudoconvex domain is zero, then the $\overline{\partial}$-Neumann operator $N_{n-1}$ is compact on $(0,n-1)$-level $L^2$-integrable forms.

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Yue Zhang. 2019-03-11. Hausdorff-$(2n-2)$ dimensional measure zero set and compactness of the $\overline{\partial}$-Neumann operator on $(0,n-1)$ forms. https://arxiv.org/abs/1903.04112

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