A direct proof of one Gromov's theorem

2008/02/01 by Yu. D. Burago, Burago, Yu. D., S. G. Malev +5
Mathematics · #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.DG #math.MG #msc:53C21

paper · pdf · doi:10.48550/arxiv.0802.0098

arxiv created 2008/02/01 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof of the Gromov theorem: For any C>0 and integer n>1 there exists a function Δ_C,n such that if the Gromov--Hausdorff distance between complete Riemannian n-manifolds V and W is not greater than δ, absolute values of their sectional curvatures |K_σ|≤ C, and their injectivity radii ≥ 1/C, then the Lipschitz distance between V and W is less than Δ_C,n(δ) and Δ_C,n→ 0 as δ→ 0.

Citations

• Riemannian center of mass and mollifier smoothing

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