Veronese minimizes normal curvatures

2024/08/12 by Anton Petrunin, Petrunin, Anton · 1 citation
Engineering · Mathematics · #53A07 #53C20 #53C35 #53C40 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2408.05909

openalex publication_date 2024/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose M is a closed submanifold in a Euclidean ball of sufficiently large dimension. We give an optimal bound on the normal curvatures, guaranteeing that M is a sphere. The border cases consist of Veronese embeddings of the four projective planes.

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