Properties of deformed mass and phase functions

Abstract

We establish basic properties of the deformed mass and phase functions on the space of stability conditions. We prove that these functions are continuous and deduce that the space of stability conditions admits a homeomorphic embedding into a product space of finite measures. Subsequently, we give a proof of the triangle inequality for deformed mass functions and provide estimates for the deformed mass of truncations of objects with respect to a slicing.

31 pages, 4 figures, Contains an appendix from our joint work arXiv:2501.00710, which will be removed from the latter in the forthcoming v2