2022/06/13 by Otis Chodosh, Chao Li, Chodosh, Otis +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2206.06394
We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in R4 has intrinsic cubic volume growth, provided the parametric elliptic integral is C2-close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in R4. The new proof is more closely related to techniques from the study of strictly positive scalar curvature.