arXiv research

Study spherical curves with curvature dependent on distance to a great circle.

Researchers found new functions for spherical clothoids using special functions.

PGF kernels analyze spherical data using generalized RBF kernels.

Study spherical Fourier transform on hypergeometric type harmonic manifolds.

Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$. We use the representation t…

Defines spherical type surfaces via support function and classifies them.

The Bounded Spherical Functions are determined for a Cartan Motion Group

Study biharmonic functions on vector bundles with spherical symmetry.

Paper explores neural network approximations on sphere domains.

This paper deals with some simple results about spherical functions of type $δ$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_σ$ functions.

Locally classifies 4D spherical symmetric Finsler spaces.

Existence and uniqueness of spherical helicoidal surfaces in 3-sphere via spherical curves.

Paper studies generic dynamics of MCFs with spherical singularities.

The paper classifies spherically symmetric Finsler metrics as Berwaldian or Riemannian.

Study null surfaces of pseudo-spherical curves in anti-de Sitter space.

We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of the orthogonal group O(n). We give exact parameterizations of the space of $(G,K…

The paper studies K-stability of spherical varieties and their degenerations.

Describes the space of spherical triangles on a smooth 3-manifold.

We present in this paper a \boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of threedimensional Euclidean sphere.

Bayesian approach approximates probability functions of Gaussian mixtures.

Proves Li-Yau inequality for Helfrich functional, ensuring embeddedness in spherical cases.

This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ ($κ>0$) and $H_\k^3$ ($κ<0$), to the standard {\itshape spherical wav…

Unique metric found for discrete curvature on spherical cone-metrics.

The paper studies T-tensor of spherically symmetric Finsler metrics and characterizes metrics satisfying the T-condition.

The study finds the optimal metrics for free boundary minimal surfaces in spherical caps.

We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an especially useful form of the metric of a spherically symmetric spacetime in polar-ar…

The paper explores geometric properties of interception curves on planes and spheres.

Conformal qc geometry of spherical qc manifolds are investigated. We construct the qc Yamabe operators on qc manifolds, which are covariant under the conformal qc transformations. A qc manifold is scalar positive, negative or vanishing if and only if its qc Yamabe invariant is positive, negative or zero, respectively. …

The paper verifies deep neural networks' ability to approximate functions on spheres.

Researchers found multiple spherical Ricci metrics on tori with rotational symmetry.

Paper computes stability of Q-Fano spherical varieties using test configurations and Futaki invariants.

Study on spherical conical metrics and their reducibility on compact Riemann surfaces.

Study spherical metrics on flat torus with cone singularities.

New capillary Christoffel-Minkowski problem solved for half-space.

We prove an estimate for spherical functions $\varphi_λ(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $λ$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.…

In a multi-class classification problem, it is standard to model the output of a neural network as a categorical distribution conditioned on the inputs. The output must therefore be positive and sum to one, which is traditionally enforced by a softmax. This probabilistic mapping allows to use the maximum likelihood pri…

The paper defines functions from spherical curves and chord diagrams, proving invariance under specific Reidemeister moves.

Study spherical convex bodies using $L_p$-floating areas and curvature entropy.

Study on evolutes and focal surfaces of pseudo-spherical framed immersions in anti-de Sitter space.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

In this paper we study spherically symmetric monopoles, which are critical points for the Yang-Mills-Higgs functional over a disk in 3 dimensions, with prescribed degree and covariant constant at the boundary. This is a 3-dimensional gauge-theory generalization of the Ginzburg-Landau model in 2 dimensions.

This study classifies quadric surfaces in 3-sphere as Weingarten surfaces.

The study proves rigidity and non-rigidity of spherical caps in mean curvature.

The paper extends geometric inequalities for nearly spherical sets in various space forms.

Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary s…

The study characterizes compact submanifolds with pinched Ricci curvature in Euclidean and spherical space forms.

One way to recognise an object is to study how the echo has been shaped during the interaction with the target. Wideband sonar allows the study of the energy distribution for a large range of frequencies. The frequency distribution contains information about an object, including its inner structure. This information is…

In this article we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that interpolates between the functionals for harmonic and biharmonic maps. In the case of …