Related papers: Mean surface shape of a human placenta
Umbilics are points of a surface embedded in three space where normal curvatures are independent of direction. The (in)famous Carath\'{e}odory Conjecture states that a compact simply connected embedded surface has at least two umbilic…
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in nature - are given and shown to lead to the same objects.…
Orthogonal surfaces are nice mathematical objects which have interesting connections to various fields, e.g., integer programming, monomial ideals and order dimension. While orthogonal surfaces in one or two dimensions are rather trivial…
Rotation distorts the vacuum magnetic field of a pulsar from that of a simple dipole. The effect is particularly strong close to the light cylinder, but also affects the field close to the stellar surface. We find the shape and locus of the…
This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…
This article examines the shape of a surface obtained by a hanging flexible, inelastic material with prescribed area and boundary curve. The shape of this surface, after being turned upside down, is a model for cupolas (or domes) under the…
Carath\'eodory's well-known conjecture states that every sufficiently smooth, closed convex surface in three dimensional Euclidean space admits at least two umbilic points. It has been established that the conjecture is true for all…
A spacelike surface in four-dimensional Lorentz-Minkowski spacetime through the lightcone has a meaningful lightlike normal vector field $\eta$. Several sufficient assumptions on such a surface with non-degenerate $\eta$-second fundamental…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
This paper explores the geometry of putting in the limiting case of a planar putting surface. Putts equidistant from the hole originating on an arc spanning \pm30 degrees are shown to share a common target point. Moving around the circle of…
It is common in Physiological Optics to fit the corneal and the lens surfaces to conic-based surfaces (usually ellipse-based surfaces), obtaining their characteristic radius of curvature and asphericity. Here we show that the variation in…
We consider a classical problem of a capillary neck between a parabolic body and a plane with a small amount of liquid in between. In the state of thermodynamic equilibrium, the contact area between the bodies and the liquid layer has a…
In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.
A spacelike surface S immersed in a 4-dimensional Lorentzian manifold will be said to be umbilical along a direction N normal to S if the second fundamental form along N is proportional to the first fundamental form of S. In particular, S…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with $n$ faces and boundary component lengths of order $\sqrt n$ or of lower order. Endow this…
We present a volumetric mesh-based algorithm for parameterizing the placenta to a flattened template to enable effective visualization of local anatomy and function. MRI shows potential as a research tool as it provides signals directly…
We prove existence and nonexistence results for annular type parametric surfaces with prescribed, almost constant mean curvature, characterized as normal graphs of compact portions of unduloids or nodoids in $\mathbb{R}^{3}$, and whose…
In this paper we investigate constant mean curvature surfaces with nonempty boundary in Euclidean space that meet a right cylinder at a constant angle along the boundary. If the surface lies inside of the cylinder, we obtain some results of…
Purpose: To characterize the mean topographical shape of the human limbus of a normal eye and ascertain whether it depends on age and refractive power. Setting: Academic institution. Design: Prospective case series. Methods: 74 subjects…