Limit leaves of a CMC lamination are stable
نویسندگان
چکیده
Suppose L is a lamination of a Riemannian manifold by hypersurfaces with the same constant mean curvature. We prove that every limit leaf of L is stable for the Jacobi operator. A simple but important consequence of this result is that the set of stable leaves of L has the structure of a lamination. Mathematics Subject Classification: Primary 53A10, Secondary 49Q05, 53C42
منابع مشابه
Harmonic and Invariant Measures on Foliated Spaces
We consider the family of harmonic measures on a lamination L of a compact space X by locally symmetric spaces L of noncompact type, i.e. L ∼= ΓL\G/K. We establish a natural bijection between these measures and the measures on the associated lamination by G-orbits, Ò L , which are right invariant under a minimal parabolic (Borel) subgroup B < G. In the special case when G is split, these measur...
متن کاملBending the Helicoid
We construct Colding-Minicozzi limit minimal laminations in open domains in R with the singular set of C-convergence being any properly embedded C-curve. By Meeks’ C-regularity theorem, the singular set of convergence of a Colding-Minicozzi limit minimal lamination L is a locally finite collection S(L) of C-curves that are orthogonal to the leaves of the lamination. Thus, our existence theorem ...
متن کاملEnding Laminations and Cannon-Thurston Maps
In earlier work, we had shown that Cannon-Thurston maps exist for Kleinian surface groups. In this paper we prove that pre-images of points are precisely end-points of leaves of the ending lamination whenever the Cannon-Thurston map is not one-to-one. In particular, the Cannon-Thurston map is finite-to-one. This completes the proof of the conjectural picture of Cannon-Thurston maps. In conjunct...
متن کاملTangencies between holomorphic maps and holomorphic laminations
We prove that the set of leaves of a holomorphic lamination of codimension one that are tangent to a germ of a holomorphic map is discrete. Let F be a holomorphic lamination of codimension one in an open set V in a complex Banach space B. In this paper, this means that V = W × C, where W is a neighborhood of the origin in some Banach space, and the leaves Lλ of the lamination are disjoint graph...
متن کاملEssential Laminations and Haken Normal Form
0. Introduction. The notion of (Haken) normal form w.r.t. a triangulation of a 3-manifold traces back to Kneser's work in the 1930's on surfaces in 3-manifolds. Haken studied it extensively in the 1960's, and showed [8] how to use it to create nite algorithms for the determination of various properties of embedded surfaces. This has since culminated, in the work of Jaco and Oertel [10], in an a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008