Article contents
Minimality and stability of minimal hypersurfaces in IRn
Published online by Cambridge University Press: 17 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
In this paper we show that the hypercone over S2 × S4 is strictly area-minimizing in ℝ8. We also show the existence of smooth embedded stable hypersurfaces in ℝ8 which are not area-minimizing.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 209 - 214
- Copyright
- Copyright © Australian Mathematical Society 1987
References
[1]Geometric measure theory and the calculus of variations. (Proc. Sympos. Pure Math. 44, Allard, W.K. and Almgren, F.J. Jr., Eds. American Mathematical Society, Providence, Rhode Island, 1986.)CrossRefGoogle Scholar
[2]Caffarelli, L., Hardt, R., Simon, L., “Minimal surfaces with isolated singularities”, Manuscript Math. 48 (1984), 1–18.CrossRefGoogle Scholar
[3]Hardt, R., Simon, L., “Minimizing hypersurfaces with isolated singularities”, (preprint).Google Scholar
[4]Lawson, B., “The equivalent Plateau problem and interior regularity”, Trans. Amer. Math. Soc. 173 (1972), 231–246.CrossRefGoogle Scholar
[5]Lin, F.H., “Approximation by smoothly embedded hypersurfaces with positive mean curvature”, (preprint).Google Scholar
[7]Simoes, P., “On a class of minimal cones in ℝn”, Bull. Amer. Math. Soc. 80 (1974), 488–489.Google Scholar
- 4
- Cited by