Gromov-Hausdorff and Intrinsic Flat Convergence and the Tetrahedral Property

Event time: 
Thursday, August 1, 2019 - 10:00am
LOM 206
Raquel Perales
Speaker affiliation: 
UNAM in Oaxaca
Event description: 

In this talk I will define the notion of Generalized Tetrahedral Property which extends Sormani’s Tetrahedral Property. This definition retains all the results of the original TP proven by Portegies-Sormani: it provides a lower bound on the sliced filling volume and a lower bound on the volumes of balls. Hence, sequences with uniform GTP have subsequences which converge in both Gromov-Hausdorff and Sormani-Wenger Intrinsic Flat sense to the same non-collapsed metric space. Through some examples we will see that the main motivation to extend the TP is to include Euclidean cones over metric spaces with small diameter. (Joint work with Jesús Nuñez-Zimbrón)