Bulletin of Mathematical Sciences
We aim at reviewing and extending a number of recent results addressing stability of certain geometric and analytic estimates in the Riemannian approximation of subRiemannian structures. In particular we extend the recent work of the the authors with Rea (Math Ann 357(3):1175–1198, 2013) and Manfredini (Anal Geom Metric Spaces 1:255–275, 2013) concerning stability of doubling properties, Poincare’ inequalities, Gaussian estimates on heat kernels and Schauder estimates from the Carnot group setting to the general case of Hörmander vector fields.
Heat kernels, Riemannian approximation, Subelliptic PDE, SubRiemannian geometry
Capogna, Luca and Citti, Giovanna, "Regularity for Subelliptic Pde Through Uniform Estimates in Multi-scale Geometries" (2016). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.