Volume preserving embeddings of open subsets of Rⁿ into manifolds

2001/12/23 by Felix Schlenk, Schlenk, Felix
Mathematics · #58D20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #math.DG #msc:58D20

paper · pdf · doi:10.48550/arxiv.math/0112260

6 pages

arxiv created 2001/12/23 · openalex publication_date 2001/12/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a connected smooth n-dimensional manifold M endowed with a volume form Ω, and we show that an open subset U of Rⁿ of Lebesgue measure \Vol (U) embeds into M by a smooth volume preserving embedding whenever the volume condition \Vol (U) ≤ \Vol (M,Ω) is met.

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