We address the problem of which functions can arise as Dehn functions of Kähler groups. We explain why there are examples of Kähler groups with linear, quadratic, and exponential Dehn function. We then proceed to show that there is an example of a Kähler group which has Dehn function bounded below by a cubic function and above by $n^6$. As a consequence we obtain that for a compact Kähler manifold having non-positive holomorphic bisectional curvature does not imply having quadratic Dehn function.

中文翻译：

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关于Kähler小组的Deh​​n功能

我们解决了哪些函数可以作为Kähler组的Deh​​n函数出现的问题。我们解释了为什么存在带有线性，二次和指数Dehn函数的Kähler群的例子。然后，我们继续说明存在一个Kähler群的示例，该群具有Dehn函数，该函数在下面被三次方函数限制，在上面被$ n ^ 6 $限制。结果，我们得到了对于具有非正全同两分式曲率的紧凑型Kähler流形并不意味着具有二次Dehn函数。