2025/01/31 by Theodoros Vlachos, Vlachos, Theodoros
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2502.09630
We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We show that this condition imposes strong constraints on either the topology or geometry of the submanifold. Additionally, we provide examples that demonstrate the sharpness of our result.