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Index estimates of compact hypersurfaces in smooth metric measure spaces
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- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 07 March 2024, pp. 1-19
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MINIMAL HYPERSURFACES ASYMPTOTIC TO SIMONS CONES
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 16 / Issue 1 / February 2017
- Published online by Cambridge University Press:
- 01 April 2015, pp. 39-58
- Print publication:
- February 2017
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In this paper, we prove that, up to similarity, there are only two minimal hypersurfaces in
$\mathbb{R}^{n+2}$ that are asymptotic to a Simons cone, i.e., the minimal cone over the minimal hypersurface 
$\sqrt{\frac{p}{n}}\mathbb{S}^{p}\times \sqrt{\frac{n-p}{n}}\mathbb{S}^{n-p}$ of 
$\mathbb{S}^{n+1}$ .
