Research summary

My research focuses on analysis in metric spaces (often in Carnot groups such as the Heisenberg group) and its relationship with the geometry of the space. More generally, I study geometric function theory, geometric measure theory, and harmonic analysis in metric settings.

Publication list



Active and related research questions

Whitney extensions into Carnot groups

Quantitative rectifiability in Carnot groups

BLD maps

Other questions

PhD Thesis

Analysis and Geometry in Metric Spaces: Sobolev Mappings, the Heisenberg Group, and the Whitney Extension Theorem

Doctoral Dissertation, University of Pittsburgh (2017). [link]

A geodesic path in the Heisenberg group