Embeddedness of least area minimal hypersurfaces
نویسندگان
چکیده
منابع مشابه
On Embeddedness of Area-Minimizing Disks, and an Application to Constructing Complete Minimal Surfaces
Let α be a polygonal Jordan curve in R 3 . We show that if α satisfies certain conditions, then the least-area Douglas-Radó disk in R 3 with boundary α is unique and is a smooth graph. As our conditions on α are not included amongst previously known conditions for embeddedness, we are enlarging the set of Jordan curves in R 3 which are known to be spanned by an embedded least-area disk. As an a...
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 کاملMinimal Hypersurfaces with Bounded Index
We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold (M, g), 3 ≤ n ≤ 7, can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embed...
متن کاملMinimal Hypersurfaces with Finite Index
In an article of Cao-Shen-Zhu [C-S-Z], they proved that a complete, immersed, stable minimal hypersurface M of R with n ≥ 3 must have only one end. When n = 2, it was proved independently by do Carmo-Peng [dC-P] and FischerColbrie-Schoen [FC-S] that a complete, immersed, oriented stable minimal surface in R must be a plane. Later Gulliver [G] and Fischer-Colbrie [FC] proved that if a complete, ...
متن کاملAdjusted least squares fitting of algebraic hypersurfaces
We consider the problem of fitting a set of points in Euclidean space by an algebraic hypersurface. We assume that points on a true hypersurface, described by a polynomial equation, are corrupted by zero mean independent Gaussian noise, and we estimate the coefficients of the true polynomial equation. The adjusted least squares estimator accounts for the bias present in the ordinary least squar...
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: Journal of Differential Geometry
سال: 2018
ISSN: 0022-040X
DOI: 10.4310/jdg/1538791246