Weighted Imbedding Theorems in the Space of Differential Forms
نویسندگان
چکیده
منابع مشابه
Imbedding Theorems in Differential Geometry*
The matters which I shall discuss today will be largely concerned with the general problem of imbedding a coordinate manifold of class C in a euclidean space of sufficiently many dimensions. I imagine you all have a fair idea as to what is meant by an w-dimensional manifold of class C. Briefly this may be described as a Hausdorff space each point of which admits a neighborhood homeomorphic to t...
متن کاملAhlfors Theorems for Differential Forms
and Applied Analysis 3 Let y1, . . . , yk be an orthonormal system of coordinates in R, 1 ≤ k ≤ n. Let A be a domain in R, and let B be an n − k -dimensional Riemannian manifold. We consider the manifold N A × B. 2. Boundary Sets Below we introduce the notions of parabolic and hyperbolic type of boundary sets on noncompact Riemannian manifolds and study exhaustion functions of such sets. We als...
متن کاملWeighted Decomposition Estimates for Differential Forms
Let e1, e2, . . . , en denote the standard orthogonal basis of R. Suppose that Λ Λ R is the linear space of all l-vectors, spanned by the exterior product eI ei1∧ei2∧· · ·∧eil corresponding to all ordered l-tuples I i1, i2, . . . , il , 1 ≤ i1 < i2 < · · · < il ≤ n. Throughout this paper, we always assume that Ω is an open subset of R. We use D′ M,Λ to denote the space of all differential l-for...
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 کاملRigidity Theorems on Hemispheres in Non–positive Space Forms
We study the curvature condition which uniquely characterizes the hemisphere. In particular, we prove the Min–Oo conjecture for hypersurfaces in Euclidean space and hyperbolic space.
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 Mathematical Analysis and Applications
سال: 2001
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7611