Are surface area or volume conserved during cell division?
Another PLOS One article gives evidence of change both in volume and in surface area, but it is across mitosis phases. It could still be considered constant during cytokinesis only. 

It seems that cell shape and size have important function during mitosis, according to this research. It would be interesting to investigate different models from your advisor's paper (constant maximum radius, volume or area) but starting from different shapes and sizes.