Skip to main content

Analysis and PDE Seminar

Date:
-
Location:
215 White Hall Classroom Building
Speaker(s) / Presenter(s):
Professor Luca Capogna, Worcester Polytechnic Instittute

Title:  Smoothness of isometries between subRiemannian manifolds

Abstract:  In a joint work with Enrico Le Donne (Jyvaskyla, Finland), we show that the group of isometries (i.e., distance-preserving homeomorphisms) of an equiregular subRiemannian manifold is a finite-dimensional Lie group of smooth transformations. The proof is based on a new PDE argument, in the spirit of harmonic coordinates, establishing that in an arbitrary subRiemannian manifold there exists an open dense subset where all isometries are smooth.