2013/12/18 by Martin Franzen, Franzen, Martin, Martin Franzén
Mathematics · #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #History and Theory of Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1312.5107
openalex publication_date 2013/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider flows with normal velocities equal to powers strictly larger than\none of the Gauss curvature. Under such flows closed strictly convex surfaces\nconverge to points. In his work on the square of the norm of the second\nfundamental form, Schn "urer proposes criteria for selecting quantities that\nare suitable for proving convergence to a round point. Such monotone quantities\nexist for many normal velocities, including the Gauss curvature, some powers\nlarger than one of the mean curvature, and some powers larger than one of the\nnorm of the second fundamental form. In this paper, we show that no such\nquantity exists for any powers larger than one of the Gauss curvature.\n