Curvature and symmetry of Milnor spheres.
Curvature and the equivalence problem in sub-Riemannian geometry
These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples, which...
Curvature and torsion formulas for conflict sets
Conflict set are the points at equal distance from a number of manifolds. Known results on the differential geometry of these sets are generalized and extended.
Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow
Curvature bounds for neighborhoods of self-similar sets
In some recent work, fractal curvatures and fractal curvature measures , , have been determined for all self-similar sets in , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent formulations...
Curvature computations on surfaces in -space
Curvature conditions on hypersurfaces with two distinct principal curvatures
We investigate curvature properties of hypersurfaces in semi-Riemannian spaces of constant curvature with the minimal polynomial of the second fundamental tensor of second degree. We present suitable examples of hypersurfaces.
Curvature contents of geometric spaces.
Curvature, diameter and Betti numbers.
Curvature estimate for the volume growth of globally minimal submanifolds.
Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals.
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 flows on surfaces
Prompted by recent work of Xiuxiong Chen, a unified approach to the Hamilton-Ricci and Calabi flows on a closed, compact surface is presented, recovering global existence and exponentially fast asymptotic convergence from concentration-compactness results for conformal metrics.
Curvature free volume estimates.
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 homogeneity of affine connections on two-dimensional manifolds
Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.
Curvature homogeneous riemannian manifolds
Curvature homogeneous spaces whose curvature tensors have large symmetries
We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large" Lie subalgebras of . In this paper we deal with the cases of