h型子黎曼流形的比较定理。

IF 2.1 2区数学 Q1 MATHEMATICS

Calculus of Variations and Partial Differential Equations Pub Date : 2025-01-01 Epub Date: 2025-05-05 DOI:10.1007/s00526-025-02992-w

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

引用次数: 0

摘要

在h型子黎曼流形上，我们建立了收敛于子黎曼流形的近似黎曼度量族的子hessian和子laplacian比较定理。我们还证明了一个尖锐的亚黎曼Bonnet-Myers定理，该定理推广到先前在接触流形和四元数接触流形上证明的一般情况下的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Comparison theorems on H-type sub-Riemannian manifolds.

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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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.