## stability of Riemann surface with boundary

The stability condition of Riemann surface with boundary, that is, a Riemann surface of genus $g$,$h$ boundary components, and with $n$ marked points in the interior,$m=(m_1,m_2,\ldots,m_{h})$marked points on the boundary, here $m_i$ is the number of marked points on the $i$th boundary component, such a surface is called stable if the automorphism group is finite. I am wondering if the stability condition is also equivalent to the euler characteristic, $2-2g-n-h-m/2$, is negative?

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