Singular homologically area minimizing surfaces of codimension one in Riemannian manifolds

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• 作者：Nathan Smale
• 刊名：Inventiones Mathematicae
• 出版年：1999
• 出版时间：January 1999
• 年：1999
• 卷：135
• 期：1
• 页码：145-183
• 全文大小：265 KB

文摘

For n≥7, it is shown how to construct examples of smooth, compact Riemannian manifolds (N n +1,g), with non-trivial n dimensional integer homology, such that for some Γ∈H _n (N,Z), the hypersurface (n-current) M, which minimizes area among all hypersurfaces representing Γ, has singularities. The singular set of M consists of two isolated points, and the tangent cone at these points can be prescribed as any strictly stable, strictly minimizing, regular cone. To my knowledge these are the first examples of codimension one homological minimizers with singularities.