arXiv research

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

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

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.

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.

Injectivity of geodesic ray transform on specific Finsler manifolds proven.

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.

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.

Study curvature operator on Riemannian manifolds, proving new classification results.

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, …

The paper constructs examples of coupled Dirac-Yang-Mills pairs on Riemannian manifolds.

Study spherically symmetric Finsler metrics with specific curvature properties.

We prove a trace formula for three-dimensional spherically symmetric Riemannian manifolds with boundary which satisfy the Herglotz condition: The wave trace is singular precisely at the length spectrum of periodic broken rays. In particular, the Neumann spectrum of the Laplace--Beltrami operator uniquely determines the…

We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds …

The study compares and finds Yamabe constants on warped products.

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.

Study proves rigid spectral properties of planets with metric discontinuities.

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…

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

Rigidity results are obtained for Riemannian $d$-manifolds with $\sec \geqslant 1$ and spherical rank at least $d-2>0$. Conjecturally, all such manifolds are locally isometric to a round sphere or complex projective space with the (symmetric) Fubini--Study metric. This conjecture is verified in all odd dimensions, for …

Locally classifies 4D spherical symmetric Finsler spaces.

Spherical Plateau problem studies minimal surfaces in quotients of spheres.

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.

Rigidity theorem for spherical sectors in Riemannian manifolds.

We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic manifolds satisfying the conditions of the positive mass theorem converges to hyper…

Study biharmonic functions on vector bundles with spherical symmetry.

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, …

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.

Let M be a complete Riemannian manifold whose sectional curvature is bounded above by 1. We say that M has positive spherical rank if along every geodesic one hits a conjugate point at t=π. The following theorem is then proved: If M is a complete, simply connected Riemannian manifold with upper curvature bound 1 and po…

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.