2021/06/16 by Hilário Alencar, Alencar, Hilário, Gregório Silva Neto +3
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2106.09165
This paper studies rigidity for immersed self-shrinkers of the mean curvature flow of surfaces in the three-dimensional Euclidean space ℝ3. We prove that an immersed self-shrinker with finite L-index must be proper and of finite topology. As one of consequences, there is no stable two-dimensional self-shrinker in ℝ3 without assuming properness. We conclude the paper by giving an affirmative answer to a question of Mantegazza.