相关论文: Geodesics on an arbitrary ellipsoid of revolution

In this paper, we introduce isophote curves on surfaces in Galilean 3-space. Apart from the general concept of isophotes, we split our studies into two cases to get the axis d of isophote curves lying on a surface such that d is an…

Many applications of geometry modeling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In this paper, we define the notion of the discrete geodesic curvature of a geodesic polygon on a…

We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility…

We describe a generalised method for ellipsoid fitting against a minimum set of data points. The proposed method is numerically stable and applies to a wide range of ellipsoidal shapes, including highly elongated and arbitrarily oriented…

We use "generalized" version of total variation, coarea formulas, isoperimetric inequalities to obtain sharp estimates for solutions (and for their gradients) to anisotropic elliptic equations with a lower order term, comparing them with…

We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…

We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm…

This paper generalizes the result of Elmachtoub et al to any weighted barycenter, where a transformation is considered which takes an arbitrary point of division $\xi \in (0,1)$ of the segments of a polygon with $n$ vertices. We then…

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat…

We present a geometric interpretation of integrability of geodesic flow by quadratic integrals in terms of the web theory and construct integrable billiards on surfaces admitting such integrals.

In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.

Any even function defined on 2-sphere is reconstructed from its integrals over big circles by means of the classical Funk formula. For the non-geodesic Funk transform on the sphere of arbitrary dimension, there is the explicit inversion…

An isogeny class of elliptic curves over a finite field is determined by a quadratic Weil polynomial. Gekeler has given a product formula, in terms of congruence considerations involving that polynomial, for the size of such an isogeny…

We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…

This paper discusses the geometry of a surface endowed with a slope metric. We obtain necessary and sufficient conditions for any surface of revolution to admit a strongly convex slope metric. Such conditions involve certain inequalities…

Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…

The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due…

Effective estimates for the lattice point discrepancy of certain planar and three-dimensional domains. This paper provides estimates, with explicit constants, for the lattice point discrepancy of o-symmetric ellipse discs and ellipsoids in…