We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a suitable notion of sub-Riemannian Bakry–Émery curvature. The model spaces for comparison are variational problems coming from optimal control theory. As an application we establish the sharp measure contraction property for 3-Sasakian manifolds satisfying a suitable curvature bound.

Bakry–Émery curvature and model spaces in sub-Riemannian geometry / Barilari, D.; Rizzi, L.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 377:(2020), pp. 435-482. [10.1007/s00208-020-01982-x]

Bakry–Émery curvature and model spaces in sub-Riemannian geometry

Rizzi, L.
2020

Abstract

We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a suitable notion of sub-Riemannian Bakry–Émery curvature. The model spaces for comparison are variational problems coming from optimal control theory. As an application we establish the sharp measure contraction property for 3-Sasakian manifolds satisfying a suitable curvature bound.
377
435
482
https://arxiv.org/abs/1906.08307
Barilari, D.; Rizzi, L.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/128688
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