STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION
نویسندگان
چکیده
منابع مشابه
The structure of weakly stable minimal hypersurfaces.
In this short communication, we announce results from our research on the structure of complete noncompact oriented weakly stable minimal hypersurfaces in a manifold of nonnegative sectional curvature. In particular, a complete oriented weakly stable minimal hypersurface in Rm, m > or = 4, must have only one end; any complete noncompact oriented weakly stable minimal hypersurface has only one e...
متن کاملThe structure of stable minimal hypersurfaces in IR
We provide a new topological obstruction for complete stable minimal hypersurfaces in IRn+1. For n ≥ 3, we prove that a complete orientable stable minimal hypersurface in IRn+1 cannot have more than one end by showing the existence of a bounded harmonic function based on the Sobolev inequality for minimal submanifolds [MS] and by applying the Liouville theorem for harmonic functions due to Scho...
متن کاملTo appear in J.ReineAng.Math. (Crelles) STABLE MINIMAL HYPERSURFACES IN A NONNEGATIVELY CURVED MANIFOLD
The classical Bernstein Theorem asserts that an entire minimal graph in R must be planar. This theorem was subsequently generalized to higher dimensions by the works of Fleming [10], Almgren [1], DeGiorgi [6], and Simons [23]. The final result states that an entire n-dimensional minimal graph in R must be given by a linear function over R providing that n ≤ 7. On the other hand, nonlinear entir...
متن کاملOn Finiteness of the Number of Stable Minimal Hypersurfaces with a Fixed Boundary
Can there be infinitely many minimal hypersurfaces with a given boundary in a Riemannian manifold? A number of previous results, positive and negative, already indicated that the answer depends on the definition of surface, on orientability, on stability and minimizing properties of the surface, on the smoothness and geometry of the boundary, and on the ambient manifold. 1. Finiteness for area-...
متن کاملSystolic Inequalities and Minimal Hypersurfaces
We give a short proof of the systolic inequality for the n-dimensional torus. The proof uses minimal hypersurfaces. It is based on the Schoen-Yau proof that an n-dimensional torus admits no metric of positive scalar curvature. In this paper, we give a short new proof of the systolic inequality for the ndimensional torus. Theorem 1. Let (T , g) be a Riemannian metric on the n-dimensional torus. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2005
ISSN: 1225-1763
DOI: 10.4134/ckms.2005.20.4.775