Minimal translation lengths on the curve graph of Torelli groups of partitioned surfaces

Putman introduced a notion of partitioned surface which is a surface with boundary with decoration restricting how they can be embedded into larger surfaces. Then he defined the Torelli group of a partitioned surface. In this paper, we show the minimal asymptotic translation length of Torelli groups of partitioned surfaces asymptotically behaves like the reciprocal of the Euler characteristic of the surface. This generalizes the previous result of the authors on Torelli groups for closed surfaces.