تقرير
The $\bar\partial$-problem on $Z(q)$-domains
| العنوان: | The $\bar\partial$-problem on $Z(q)$-domains |
|---|---|
| المؤلفون: | Chakrabarti, Debraj, Harrington, Phillip S., Raich, Andrew |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, 32F10, 32F32, 32W05 |
| الوصف: | Given a complex manifold containing a relatively compact $Z(q)$ domain, we give sufficient geometric conditions on the domain so that its $L^2$-cohomology in degree $(p,q)$ (known to be finite dimensional) vanishes. The condition consists of the existence of a smooth weight function in a neighborhood of the closure of the domain, where the complex Hessian of the weight has a prescribed number of eigenvalues of a particular sign, along with good interaction at the boundary of the Levi form with the complex Hessian, encoded in a subbundle of common positive directions for the two Hermitian forms. Comment: 29 pages. Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.04756 |
| رقم الأكسشن: | edsarx.2403.04756 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |