论文标题
温带电流的浓汤
A Dolbeault lemma for temperate currents
论文作者
论文摘要
我们考虑了一个复杂的Stein歧管$ x $ dimension $ n $的有界开放式Stein子集$ω$。我们证明，如果$ f $是$ x $ bidegree $（p，q+1）$，$ \ bar \ partial $ clucted在$ω$上的$，我们可以在$ x $ bidegree $（p，q）上找到当前的$ u $（p，q）$，这是等式$ \ bar \ bar \ poartial u = f $ in $ = f $的解决方案。换句话说，我们证明了$ω$上的温带电流的多尔贝特综合体（即$ω$的电流延伸到$ x $上的电流）集中在度数$ 0 $中。此外，如果$ f $是$ x = c^n $的当前订单$ k $，那么我们可以找到一个解决方案$ u $，这是$ k+2n+1 $的$ c^n $上的当前。
We consider a bounded open Stein subset $Ω$ of a complex Stein manifold $X$ of dimension $n$. We prove that if $f$ is a current on $X$ of bidegree $(p,q+1)$, $\bar\partial$-closed on $Ω$, we can find a current $u$ on $X$ of bidegree $(p,q)$ which is a solution of the equation $\bar\partial u=f$ in $Ω$. In other words, we prove that the Dolbeault complex of temperate currents on $Ω$ (i.e. currents on $Ω$ which extend to currents on $X$) is concentrated in degree $0$. Moreover if $f$ is a current on $X= C^n$ of order $k$, then we can find a solution $u$ which is a current on $C^n$ of order $k+2n+1$.
