2011/10/16 by Weiqiang Wu, Wu, Weiqiang
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.GT
paper · pdf · doi:10.48550/arxiv.1110.3541
openalex publication_date 2011/10/16 · arxiv created 2012/07/21 · arxiv updated 2012/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies certain embedded spheres in closed affine manifolds. For n ≥ 3, we investigate the dome bodies in a closed affine n-manifold M with its boundary homeomorphic to a sphere under the assumption that a developing map restricted to a component of ∂M is an embedding onto a strictly convex sphere in \mathbbAn. By using the recurrent property of an incomplete geodesic we show that dome bodies are compact. Then a maximal dome body is a closed solid ball bounded by a component of ∂M, and hence equals M. The main theorem is that the standard ball in an affine space can only bound one compact affine manifold inside, namely the solid ball.