Curvature Estimates for Immersions of Minimal Surface Type via Uniformization and Theorems of Bernstein Type.
Curvature estimates for minimal hypersurfaces in singular spaces.
Curvature estimates for minimal surfaces in -manifolds
Curvature functionals for curves in the equi-affine plane
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.
Curvature Properties of 6-Parametric robot manipulators.
Curvatures and Curves in Hilbert Space.
Curvatures of conflict surfaces in Euclidean 3-space
This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane, established by Siersma [3]. In the present case a conflict surface arises, equidistant from the given convex sets. The Gaussian, mean curvatures and the location of umbilic points on the conflict surface are determined here. Initial results on the Darbouxian type of umbilic points on conflict surfaces are also established. The results are expressed in terms of the principal...
Curve shortening flow and the Banchoff-Pohl inequality on surfaces of nonpositive curvature.
Curve shortening makes convex curves circular.
Curve shortening on surfaces
Curved Casimir operators and the BGG machinery.
Curves and surfaces in hyperbolic space
In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.
Curves in Banach spaces which allow a parametrization or a parametrization with finite convexity
We give a complete characterization of those (where is a Banach space) which allow an equivalent parametrization (i.e., a parametrization whose derivative has bounded variation) or a parametrization with bounded convexity. Our results are new also for . We present examples which show applicability of our characterizations. For example, we show that the and parametrization problems are equivalent for but are not equivalent for .
Curves in the lightlike cone.
Curves of constant breadth
Curves with finite turn
In this paper we study the notions of finite turn of a curve and finite turn of tangents of a curve. We generalize the theory (previously developed by Alexandrov, Pogorelov, and Reshetnyak) of angular turn in Euclidean spaces to curves with values in arbitrary Banach spaces. In particular, we manage to prove the equality of angular turn and angular turn of tangents in Hilbert spaces. One of the implications was only proved in the finite dimensional context previously, and equivalence of finiteness...
Cyclic actions on - and -bundles over
Cyclic structures of geometric objects involving a connection and Lie derivatives
Cyclides of rotation of the Galileian space . (Drehzykliden des galileischen Raumes .)
Cylindrical Tzitzeica curves implies forced harmonic oscillators.