Techniques for proving infinitesimal Hilbertianity

Abstract: A metric space is said to be "universally infinitesimally Hilbertian" if, when endowed with any arbitrary Radon measure, its associated 2-Sobolev space is Hilbert. For instance, all (sub)Riemannian manifolds and CAT(K) spaces have this property. In this talk, we will illustrate three different strategies to prove the universal infinitesimal Hilbertianity of the Euclidean space, which is the base case and where all the known approaches work. The motivations come, among others, from the study of rectifiable metric measure spaces, of metric-valued harmonic maps, and of variational problems (such as models representing low-dimensional elastic structures).

differential geometrymetric geometry

Audience: researchers in the topic

mms&convergence

Series comments: Join Zoom Meeting: cuaieed-unam.zoom.us/j/84506421108?pwd=cjM5Q3NZR2gyQnV3Sjdqci80RkVSUT09

Meeting ID: 845 0642 1108 Passcode: 182795