Conventional physical dogma, justified by the local success of Newtonian dynamics for particles, assigns a Euclidean metric with signature (plus, plus, plus) to the three spatial dimensions. Minimal surfaces are of zero mean curvature and negative Gauss curvature in a Euclidean space, which supports affine evolutionary processes. However, experimental evidence now indicates that the non-affine ...

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we ...

0. Introduction. It is a well-known consequence of the classical uniformization theorem that there is a metric with constant Gaussian curvature in each conformal class of any compact Riemann surface. It is natural to ask how to generalize this classical uniformization theory to compact surfaces with conical singularities and with nonempty boundary, or to find a “best metric” on such surfaces. H...

We study the Weil-Petersson geometry for holomorphic families of Riemann Surfaces equipped with the unique conical metric of constant curvature −1.

We study the asymptotic behaviour of p-capacitary potential and weak inverse mean curvature flow a bounded set along ends an asymptotically conical Riemannian manifolds with nonnegative Ricci curvature.

Circular meshes are quadrilateral meshes all of whose faces possess a circumcircle,whereas conicalmeshes areplanar quadrilateralmeshes where the faces which meet in a vertex are tangent to a right circular cone. Both are amenable to geometricmodeling – recently surface approximation and subdivision-like refinement processes have been studied. In this paper we extend the original defining proper...

We discuss the variational properties of the unique conical metric of constant curvature −1 associated to a compact Riemann surface together with a weighted divisor.  2005 Elsevier Inc. All rights reserved.

A compact, highly sensitive optical fiber displacement and curvature radius sensor is presented. The device consists of an adiabatic bi-conical fused fiber taper spliced to a single-mode fiber (SMF) segment with a flat face end. The bi-conical taper structure acts as a modal coupling device between core and cladding modes for the SMF segment. When the bi-conical taper is bent by an axial displa...