Abstract
AbstractWe show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in$\mathbf {R}^4$has intrinsic cubic volume growth, provided the parametric elliptic integral is$C^2$-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$\mathbf {R}^4$. The new proof is more closely related to techniques from the study of strictly positive scalar curvature.
Publisher
Cambridge University Press (CUP)
Subject
Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Analysis
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