Related papers: The analytic torsion of a cone over a sphere
We present new mathematical alternatives for explaining rotation curves of spiral galaxies in the MOND context. For given total masses, it is shown that various mathematical alternatives to MOND, while predicting flat rotation curves for…
We show that the torsion of any simple closed curve $\Gamma$ in Euclidean 3-space changes sign at least $4$ times provided that it is star-shaped and locally convex with respect to a point $o$ in the interior of its convex hull. The latter…
We construct and classify, in the case of two complex dimensions, the possible tangent cones at points of limit spaces of non-collapsed sequences of K\"ahler-Einstein metrics with cone singularities.
An extra large metric is a spherical cone metric with all cone angles greater than 2 pi and every closed geodesic longer than 2pi. We show that every two-dimensional extra large metric can be triangulated with vertices at cone points only.…
This paper studies length estimates for trajectories on flat cone surfaces in terms of their self-intersection numbers. For an area-one flat cone surface, we obtain a lower bound for the length of a trajectory, with constants depending only…
We obtain an analytical solution for the weighted Fermat-Torricelli problem for an equilateral geodesic triangle A_1A_2A_3 which is composed by three equal geodesic arcs (sides) of length Pi/2 for given three positive unequal weights that…
The spanning surface defect uses spanning surfaces of a knot in the $3$-sphere to measure how far a knot is from being alternating. We refine the spanning surface defect and extend the definition to take into account surfaces in the…
In order to study gravitational waves in any realistic astrophysical scenario, one must consider geometry perturbations up to second order. Here, we present a general technique for studying linear and quadratic perturbations on a spacetime…
The tilt-over mode in a precessing triaxial ellipsoid is studied theoretically and numerically. Inviscid and viscous analytical models previously developed for the spheroidal geometry by Poincar\'e [Bull. Astr. 27, 321 (1910)] and Busse [J.…
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly…
We describe an algorithm that provably computes the rational torsion subgroup of the Jacobian of a curve without relying on height bounds. Instead, the strategy is to find upper bounds for the torsion subgroup using reduction modulo primes,…
We apply recent circle tangency estimates due to Pramanik--Yang--Zahl to prove sharp weighted Fourier extension estimates for the cone in $\mathbb{R}^3$ and $1$-dimensional weights. The idea of using circle tangency estimates to study…
Mordell curves over a number field $K$ are elliptic curves of the form $ y^2 = x^3 + c$, where $c \in K \setminus \{ 0 \}$. Let $p \geq 5$ be a prime number, $K$ a number field such that $[K:\mathbb{Q}] \in \{ 2p, 3p \}$ and let $E$ be a…
We study the multi-height distribution of rational points of smooth, projective and split toric varieties over $\mathbf{Q}$ using the lift of the number of points to universal torsors.
This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections.…
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These…
The paper studies the problem of prescribing positive cross curvature on the three-dimensional sphere. We produce several existence results and an example of non-uniqueness, disproving a conjecture of Hamilton's.
The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation…
We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…
In this paper we study the spherical convexity of quadratic functions on spherically convex sets. In particular, conditions characterizing the spherical convexity of quadratic functions on spherical convex sets associated to the positive…