Subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces with isolated singularities

Dariush Ehsani

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arXiv · 2202.10867

Subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces with isolated singularities

Dariush Ehsani

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Abstract

We obtain subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces embedded in $\mathbb{C}^n$ with isolated singularities. $W^{\epsilon}$ Sobolev norms of a form, $f$, for $0< \epsilon < 1$ are estimated in terms of weighted $L^2$ norms of $\bar{\partial} f$ and $\bar{\partial}^{\ast}f$, with weights which vanish at the singularities, as well as weighted $L^2$ norms of $f$, with weights which blow up at the singularities.

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BibTeX RIS

Dariush Ehsani. 2022-02-22. Subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces with isolated singularities. https://arxiv.org/abs/2202.10867

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