相关论文: The analytic torsion of a cone over a sphere

The formula for analytic torsion of a cone in even dimensions is comprised of three terms. The first two terms are well understood and given by an algebraic combination of the Betti numbers and the analytic torsion of the cone base. The…

We provide a simple topological derivation of a formula for the Reidemeister and the analityc torsion of spheres.

We study the analytic torsion of the cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the…

The analytic torsion is computed on fixed-point free and non fixed-point free factors (tessellations) of the three--sphere. We repeat the standard computation on spherical space forms (Clifford-Klein spaces) by an improved technique. The…

In this paper we study the analytic torsion of an odd-dimensional manifold with isolated conical singularities. First we show that the analytic torsion is invariant under deformations of the metric which are of higher order near the…

We present a direct proof that the Anomaly Boundary term of J. Br\"unning and X. Ma generalizes to the cases of the cone over a $m$-dimensional sphere.

We study the Erdos distance conjecture on the unit sphere in three dimensions using Fourier analytic methods.

The manuscript provides formulas for the volume of a body defined by the intersection of a solid cone and a solid sphere as a function of the sphere radius, of the distance between cone apex and sphere center, and of the cone aperture…

The purpose of this article is to give an explicit formula for all curves of constant torsion $\tau$ in the unit two-sphere $S^2(1)$. These curves and their basic properties have been known since the 1890's, and some of these properties are…

We describe the curves of constant (geodesic) curvature and torsion in the three-dimensional round sphere. These curves are the trajectory of a point whose motion is the superposition of two circular motions in orthogonal planes. The global…

We study the Reidemeister torsion and the analytic torsion of the $m$ dimensional disc in the Euclidean $m$ dimensional space, using the base for the homology defined by Ray and Singer in \cite{RS}. We prove that the Reidemeister torsion…

This paper presents formulae for calculation the solid angle of intersecting spherical caps, conical surfaces and polyhedral cones.

We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the…

We prove the equality of the $L^2$-analytic torsion and the intersection R torsion of the even dimensional finite metric cone over an odd dimensional compact manifold.

We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in $d$ dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For $d=2$, for…

We prove a sharp square function estimate for the cone in $\mathbb{R}^3$ and consequently the local smoothing conjecture for the wave equation in $2+1$ dimensions.

We investigate the limit the R torsion of a conical frustum as one of the basis is shrunk to a point. We show that, if we take suitable regularization, such a limit gives the intersection torsion of the resulting cone.

We establish Conway's thrackle conjecture in the case of spherical thrackles; that is, for drawings on the unit sphere where the edges are arcs of great circles.

We determine all the possible torsion groups of elliptic curves over cyclic cubic fields, over non-cyclic totally real cubic fields and over complex cubic fields.

We provide a general formulation of the spin-orbit coupling on a 2D curved surface. Considering the wide applicability of spin-orbit effect in spinor-based condensed matter physics, a general spin-orbit formulation could aid the study of…