Index estimates for free boundary minimal hypersurfaces
نویسندگان
چکیده
منابع مشابه
Minimal 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 کاملMinimal hypersurfaces in H × R, total curvature and index
In this paper, we consider minimal hypersurfaces in the product space Hn × R. We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal hypersurfaces with finite total curvature. This assumption implies that the corresponding curvature goes to zero uniformly at infinity. We show that surfaces with finite total int...
متن کاملUniqueness Theorems for Free Boundary Minimal Disks in Space Forms
We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...
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: Mathematische Annalen
سال: 2017
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-017-1549-8