Stable anisotropic minimal hypersurfaces in
We 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 hy...
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| Published in | Forum of mathematics. Pi Vol. 11 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
02.02.2023
|
| Online Access | Get full text |
| ISSN | 2050-5086 2050-5086 |
| DOI | 10.1017/fmp.2023.1 |
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| Summary: | We 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. |
|---|---|
| ISSN: | 2050-5086 2050-5086 |
| DOI: | 10.1017/fmp.2023.1 |