Related papers: Surface Area of Ellipsoids

We present a survey article about the geometry of convex bodies on the $d$-dimensional sphere $S^d$. We concentrate on the results based on the notion of the width of a convex body $C \subset S^d$ determined by a supporting hemisphere of…

We show some characterizations of hyperspheres in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with intrinsic and extrinsic properties such as the $n$-dimensional area of the sections cut off by hyperplanes, the…

We discuss a general formula for the area of the surface that is generated by a graph $[t_0, t_1] \to \mathbb R^2$ sending $t \mapsto \bigl(x(t), y(t) \bigr)$ revolved around a general line $L: A x + B y = C$. As a corollary, we obtain a…

We present a model for computing the surface force density on a fluid ellipsoid in simple shear flow, which we derive by coupling existing models for the shape of a fluid droplet and the surface force density on a solid ellipsoid. The…

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean $(n+1)-$space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized…

This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads…

We consider the problem of estimating the perimeter of a smooth domain in the plane based on a sample from the uniform distribution over the domain. We study the performance of the estimator defined as the perimeter of the alpha-shape of…

In this paper we describe the $\epsilon$-isothermic surfaces in the pseudo-Euclidean 3-space and we obtain the pseudo-Calapso equation. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal…

We prove rigidity for hypersurfaces with boundary in the unit $(n+1)$-sphere with scalar curvature bounded below by $n(n-1)$. Under appropriate boundary conditions, the hypersurfaces are shown to be part of the equatorial spheres. The lower…

We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic…

In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.

Measures of erythrocytes volume and surface are helpful in several physiological studies, both for zoologists and veterinarians. Whilst diameter and volume are assessed with ease from observations of blood smears and complete blood count,…

An asymptotic formula is proved for the expected $T$-functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere in $\mathbb{R}^n$ according to an arbitrary positive…

In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space $E^3$. We study the geometry of such surfaces by calculating the Gaussian and mean curvatures to determine when the surface is flat or minimal…

Let $f$ be an analytic function on the unit disc which is in the Dirichlet class, so the Euclidean area of the image, counting multiplicity, is finite. The Euclidean length of a radial arc of hyperbolic length $\rho$ is then $o(\rho^1/2)$.…

This survey paper concerns elliptic surfaces with section. We give a detailed overview of the theory including many examples. Emphasis is placed on rational elliptic surfaces and elliptic K3 surfaces. To this end, we particularly review the…

There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

In Euclidean space, we investigate surfaces whose mean curvature $H$ satisfies the equation $H=\alpha\langle N,\mathbf{x}\rangle+\lambda$, where $N$ is the Gauss map, $\mathbf{x}$ is the position vector and $\alpha$ and $\lambda$ are two…

This paper introduces a new analytical method for the determination of the coverage area modeling the Earth as an oblate ellipsoid of rotation. Starting from the knowledge of the satellite's position vector and the direction of the…