3 papers
math.GT2026
Spaces with Multiple Conical Singularities and their Stratifications
Mohammad Alattar, Lewis Tadman
In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and…
math.GT2024
Deformations of Lipschitz Homeomorphisms
Mohammad Alattar
We obtain the Lipschitz analogues of the results Perelman used from Siebenmann's deformation of homeomorphism theory in his proof of the stability theorem. Consequently, we obtain…
math.MG2024
Stability and Finiteness of Wasserstein Spaces
Mohammad Alattar
Under Gromov--Hausdorff convergence, and equivariant Gromov--Hausdorff convergence, we prove stability results of Wasserstein spaces over certain classes of singular and non-singul…