4 papers
A categorical perspective on extended metric-topological spaces
Enrico Pasqualetto, Timo Schultz, Janne Taipalus
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its dist…
Synthetic approaches to Ricci flows
Matthias Erbar, Marco Flaim, Eric Hupp +3
We review different notions of synthetic Ricci flow that apply to time-dependent families of metric measure spaces and which are based on properties of the heat flow, ideas from op…
Synthetic notions of Ricci flow for metric measure spaces
Matthias Erbar, Zhenhao Li, Timo Schultz
We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of d…
Metric conditions that guarantee existence and uniqueness of Optimal Transport maps
Shucheng Li, Mattia Magnabosco, Timo Schultz
We investigate metric conditions that allow to prove existence and uniqueness of a map solving the Monge problem between two marginals in a metric (measure) space, proving two main…