Image formation is described by means of modern geometry in terms of topological and geometric curvatures. These curvatures and derived equivalences are a quantisation of the set of rules for constructing the image in particular along discontinuity, singularity and bifurcation sets. A simpliication of the set of construction rules is proposed by applying a dynamic scale-space paradigm. Dynamic ...

We investigate the asymptotic behavior of curvatures of the Weil-Petersson metric in Teichmüller space. We use a pointwise curvature estimate to study directions, in the tangent space, of extremely negative curvature and directions of asymptotically zero curvatures.

The impairment of vision, especially the blindness, generates specific kind of locomotion with characteristic bending of body, stepping gate, short steps etc. (Dziedzic, 1980). It creates, among other things, characteristic anterior and backward curvatures of spine. Sport activity by playing sport games influences the values of the curvatures in sagittal plane only in small part. However the ef...

Abstract. We construct a sequence of compact embedded minimal disks in the unit ball in Euclidean 3-space whose boundaries are in the boundary of the ball and where the curvatures blow up at every point of a line segment of the vertical axis, extending from the origin. We further study the transversal structure of the minimal limit lamination and find removable singularities along the line segm...

Aging is associated with alterations in thoracolumbar curvatures and respiratory function. Research information regarding the correlation between thoracolumbar curvatures and a comprehensive examination of respiratory function parameters in older adults is limited. The aim of the present study was to examine the correlation between thoracolumbar curvatures and respiratory function in community-...

An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 256(3) grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfa...

We study principal curvatures of fibers and Heeagaard surfaces smoothly embedded in hyperbolic 3-manifolds. It is well known that a fiber or a Heegaard surface in a hyperbolic 3-manifold cannot have principal curvatures everywhere less than one in absolute value. We show that given an upper bound on the genus of a minimally embedded fiber or Heegaard surface and a lower bound on the injectivity...

Suppose that S is given a generic Riemannian metric with sectional curvatures which satisfy a suitable pinching condition formulated in terms of complex sectional curvatures. This pinching condition is satisfied by manifolds whose real sectional curvatures Kr(σ) satisfy 1/2 < Kr(σ) ≤ 1. Then the number of minimal two spheres of Morse index λ, for n − 2 ≤ λ ≤ 2n− 6, is at least p3(λ− n+ 2), wher...

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces’ areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature.We dis...