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Comparison theorems on H-type sub-Riemannian manifolds

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arxiv 1909.03532 v2 pith:ESQ6YOVZ submitted 2019-09-08 math.DG

Fabrice Baudoin , Erlend Grong , Luca Rizzi , Sylvie Vega-Molino This is my paper · ORCID
classification math.DG
keywords sub-riemannianmanifoldscomparisoncontacth-typetheoremsapproximatingbonnet-myers
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On H-type sub-Riemannian manifolds we establish sub-Hessian and sub-Laplacian comparison theorems which are uniform for a family of approximating Riemannian metrics converging to the sub-Riemannian one. We also prove a sharp sub-Riemannian Bonnet-Myers theorem that extends to this general setting results previously proved on contact and quaternionic contact manifolds.

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  1. The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds

    math.FA 2019-08 accept novelty 8.0 of 10

    A quasi-convex relaxation of the curvature-dimension condition gives dimension-independent Poincaré and log-Sobolev constants on Heisenberg groups and other sub-Riemannian manifolds, up to a universal factor.

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