2022/11/25 by Jacob Bernstein, Bernstein, Jacob, Arunima Bhattacharya +1
Engineering · Mathematics · #53C44 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2211.14257
openalex publication_date 2022/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a family of functionals on submanifolds of Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy of submanifolds of Euclidean space. We show that these functionals are monotone under mean curvature flow under natural conditions. As a consequence, we obtain sharp lower bounds on these entropies for certain closed hypersurfaces and observe a novel rigidity phenomenon.