arXiv research

The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.

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

The paper characterizes spherically symmetric metrics with scalar curvature.

The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.

Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically symmetric metrics with constant Ricci curvature and constant flag curvature.

The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.

In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing projectively as well as dually flat spherically symmetric Finsler metrics. Finally, …

Study spherically symmetric Finsler metrics with specific curvature properties.

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

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…

Derives a formula for fermion dimensions in spherically symmetric monopole backgrounds.

The study proves strong cosmic censorship violation for spherically symmetric dust clouds.

Locally classifies 4D spherical symmetric Finsler spaces.

In this paper we classify the simply connected, spherical pseudohermitian manifolds whose Webster metric is CR-symmetric.

In this paper, we classify the spherically symmetric Berwald metrics in $\mathbb{R}^n$. For the spherically symmetric Landsberg metrics, we prove that there do not exist any non-Berwald metrics among the regular case. The partial differential equation systems which can respectively characterize the spherically symmetri…

Characterizes spherical Finsler metrics satisfying a specific condition.

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

We give lower and upper bounds for the first eigenvalue of geodesic balls in spherically symmetric manifolds. These lower and upper bounds are $C^{0}$-dependent on the metric coefficients. It gives better lower bounds for the first eigenvalue of spherical caps than those from Betz-Camera-Gzyl.

New exact spherically symmetric vacuum solutions found in Finsler gravity.

The paper classifies spherically symmetric sprays and their curvature properties.

In this paper, we give the general form of spherically symmetric Finsler metrics in $R^n$ and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The necessary and sufficient conditions that projective Finsler metrics with spherical sym…

We prove that M. Kramer's classification of list of spherical pairs coincides with that for weakly symmetric spaces by examining the linear isotropy representation of the corresponding homogeneous space associated to each pair.

In this paper, we show that small spherical soap bubbles in irreducible simply connected symmetric spaces of rank greater than one are constructed from the limits of a certain kind of modified mean curvature flows starting from small spheres in the Euclidean space of dimension equal to the rank of the symmetric space, …

We obtain lower bounds for the first Laplacian eigenvalues of geodesic balls of spherically symmetric manifolds. These lower bounds are only $C^{0}$ dependent on the metric coefficients.

Study of spacelike singularities in spherical spacetimes with scalar matter.

Study proposes initial data sets for solving gravitational equations, proving energy estimates.

Unique solutions found for wave-like decaying null infinity equations.

Smooth minimizers found for Willmore energy surfaces.

We classify hyperbolic monopoles with continuous symmetries and construct new examples.

New symmetries found in Riemann-Cartan geometries.

In this paper, we investigate the spherically symmetric Finsler metrics with isotropic S-curvature and obtain a characterized equation. As an application, we prove that these metrics with Douglas type must be Randers metrics or Berwald metrics. This result leads to two classification theorems.

Study integral kernels on complex symmetric spaces and their Dyson Brownian Motion applications.

Unique global solutions found for specific initial data.

We solve spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in Schwarzschild spacetimes and analyze their asymptotic behavior near the coordinate singularity r = 2M. Furthermore, we join SS-CMC hypersurfaces in the Kruskal extension to obtain complete ones and discuss the smooth properties.

We investigate projective spherically symmetric Finsler metrics with constant flag curvature in $R^n$ and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk are found to have constant negative flag curvature.

Injectivity of geodesic ray transform on specific Finsler manifolds proven.

Kähler-Einstein metrics found on special types of symmetric varieties.

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…

We first summarize the characterization of smooth spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in the Schwarzschild spacetime and Kruskal extension. Then use the characterization to prove special SS-CMC foliation property, and verify part of the conjecture by Malec and Ó Murchadha in t…

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.

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a metric connection. The tangent bundle of $E$ admits a canonical decomposition and t…

The paper studies the holonomy of spherically symmetric Finsler metrics.

Study proves rigid spectral properties of planets with metric discontinuities.

Study shows directional convergence for neural networks under spherical symmetry.

It is known that every ribbon category with unimodality allows symmetrized $6j$-symbols with full tetrahedral symmetries while a spherical category does not in general. We give an explicit counterexample for this, namely the category $\mathcal{E}$. We define the mirror conjugate symmetry of $6j$-symbols instead and sho…

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.

We construct an example of a spherically symmetric black hole interior in which there is NO (spherically symmetric) marginally trapped tube asymptotic to the event horizon. The construction uses a self-gravitating massive scalar field matter model, and the key condition we impose is that the scalar field $φ$ be bounded…

Proves inequality for special 3D shapes, generalizing to non-symmetric ones.