Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · dg-ga/9709001

The structure of stable minimal hypersurfaces in R^n

Huai-Dong Cao·Ying Shen·Shunhui Zhu
View original source ↗Read source document ↗Export metadata ↓

Abstract

We provide a new topological obstruction for complete stable minimal hypersurfaces in R^n. For $n\geq 4$, we prove that any complete orientable stable hypersurfaces in R^n has only one end. This follows from a more general analytic theorem we prove in the paper.

Explore related subjects

dg-gamath.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Huai-Dong Cao, Ying Shen, Shunhui Zhu. 1997-08-30. The structure of stable minimal hypersurfaces in R^n. https://arxiv.org/abs/dg-ga/9709001

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2025

Long time behavior of leafwise heat flow for Riemannian foliations

For any Riemannian foliation F on a closed manifold M with an arbitrary bundle-like metric, leafwise heat flow of differential forms is proved to preserve smoothness on M at infinite time. This result and its proof have consequences about the space of bundle-like metrics on M, about the dimension of the space of leafwise harmonic forms, and mainly about the second term of the differentiable spectral sequence of F.

dg-ga↗
arXiv2018

A Simple Geometric Representative for $μ$ of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $μ$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p) $ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.

dg-ga↗
arXiv2013

Moduli spaces of PU(2)-monopoles

The goal of this article was the S^1-equivariant transversality-problem and the compactification-problem for the moduli spaces of (perturbed) PU(2)-monopoles. A substantially improved version entitled "Moduli spaces of PU(2)-monopoles (revised version)" which gives simpler, clearer proofs of the transversality results, has been published on arxiv in June 99 and appeared in Asian J. Math, see Moduli spaces of PU(2)-Monopoles, Asian J. Math. Vol. 4, No. 2 (2000), 391-436.

dg-ga↗