Baudoin Fabrice, Grong Erlend, Rizzi Luca, Vega-Molino Sylvie
Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark.
Department of Mathematics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway.
Calc Var Partial Differ Equ. 2025;64(5):143. doi: 10.1007/s00526-025-02992-w. Epub 2025 May 5.
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.
在H型次黎曼流形上，我们建立了次黑塞比较定理和次拉普拉斯比较定理，这些定理对于一族收敛到次黎曼度量的逼近黎曼度量是一致的。我们还证明了一个精确的次黎曼-邦尼特-迈尔斯定理，该定理将先前在接触流形和四元数接触流形上证明的结果推广到了这个一般情形。
