The Library
Incompatible elasticity and the immersion of non-flat Riemannian manifolds in Euclidean space
Tools
Kupferman, Raz and Shamai, Yossi (2012) Incompatible elasticity and the immersion of non-flat Riemannian manifolds in Euclidean space. Israel Journal of Mathematics, Volume 190 (Number 1). pp. 135-156. doi:10.1007/s11856-011-0187-1 ISSN 0021-2172.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1007/s11856-011-0187-1
Abstract
We study a geometric problem that originates from theories of nonlinear elasticity: given a non-flat n-dimensional Riemannian manifold with boundary, homeomorphic to a bounded subset of ℝ n , what is the minimum amount of deformation required in order to immerse it in a Euclidean space of the same dimension? The amount of deformation, which in the physical context is an elastic energy, is quantified by an average over a local metric discrepancy. We derive an explicit lower bound for this energy for the case where the scalar curvature of the manifold is non-negative. For n = 2 we generalize the result for surfaces of arbitrary curvature.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Israel Journal of Mathematics | ||||
Publisher: | Springer | ||||
ISSN: | 0021-2172 | ||||
Official Date: | 2012 | ||||
Dates: |
|
||||
Volume: | Volume 190 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 135-156 | ||||
DOI: | 10.1007/s11856-011-0187-1 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |