Solutions of the $\bar \partial $-equation on Stein and on K\"ahler manifold with compact support
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T02:55:32Z | |
| dc.date.available | 2024-04-04T02:55:32Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192371 | |
| dc.description.abstractEn | We study the $\bar \partial $-equation first in Stein manifold then in complete K\"ahler manifolds. The aim is to get $L^{r}$ and Sobolev estimates on solutions with compact support. In the Stein case we get that for any $(p,q)$-form $\omega $ in $L^{r}$ with compact support and $\bar \partial $-closed there is a $(p,q-1)$-form $u$ in $W^{1,r}$ with compact support and such that $\bar \partial u=\omega .$ In the case of K\"ahler manifold, we prove and use estimates on solutions on Poisson equation with compact support and the link with $\bar \partial $ equation is done by a classical theorem stating that the Hodge laplacian is twice the $\bar \partial $ (or Kohn) Laplacian in a K\"ahler manifold. This uses and improves, in special cases, our result on Andreotti-Grauert type theorem. | |
| dc.language.iso | en | |
| dc.title.en | Solutions of the $\bar \partial $-equation on Stein and on K\"ahler manifold with compact support | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1902.02724 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-02505591 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02505591v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AMAR,%20Eric&rft.genre=preprint |
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