Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed Curves
نویسنده
چکیده
The problem of minimal distortion bending of smooth compact embedded connected Riemannian n-manifolds M and N without boundary is made precise by defining a deformation energy functional Φ on the set of diffeomorphisms Diff(M,N). We derive the Euler-Lagrange equation for Φ and determine smooth minimizers of Φ in case M and N are simple closed curves. MSC 2000 Classification: 58E99
منابع مشابه
Bending 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 کاملSets of Constant Distance from a Compact Set in 2-manifolds with a Geodesic Metric
Let (M, d) be a complete topological 2-manifold, possibly with boundary, with a geodesic metric d. Let X ⊂ M be a compact set. We show that then for all but countably many ε each component of the set S(X, ε) of points ε-distant from X is either a point, a simple closed curve disjoint from ∂M or an arc A such that A ∩ ∂M consists of both endpoints of A, and arcs and simple closed curves are dens...
متن کاملClosed minimal surfaces of high Morse index in manifolds of negative curvature
We use Bott’s equivariant Morse theory to show that compact Riemannian three-manifolds with negative sectional curvature possess closed minimal surfaces of arbitrarily high Morse index. 1 Sources of noncompactness for parametrized minimal surfaces In this article, we apply the theory of parametrized two-dimensional minimal surfaces in a compact n-dimensional Riemannian manifold (M, 〈·, ·〉) to t...
متن کاملExperimental Investigations into the Collapse of Simple and Reinforced Thin-Walled Channel Beams under Bending Loads
In this paper, collapse behavior of simple and reinforced thin-walled channel- section beams, subjected to three- point bending, is investigated. Many simple channel- section beams of different geometry and some reinforced ones were tested, and their strengths after collapse were obtained thoroughly. Since the available theories in this area are complicated and little attention has been paid to...
متن کاملExperimental Investigations into the Collapse of Simple and Reinforced Thin-Walled Channel Beams under Bending Loads
In this paper, collapse behavior of simple and reinforced thin-walled channel- section beams, subjected to three- point bending, is investigated. Many simple channel- section beams of different geometry and some reinforced ones were tested, and their strengths after collapse were obtained thoroughly. Since the available theories in this area are complicated and little attention has been paid to...
متن کامل