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<p>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.</p>

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Comparison theorems on H-type sub-Riemannian manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月5日

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  • Fabrice Baudoin,
  • Erlend Grong,
  • Luca Rizzi,
  • Sylvie Vega-Molino

摘要

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.