Related papers: Sharp bounds on the critical stability radius for …
The accelerating behavior of cosmic fluid opposes to the gravitational attraction, at present epoch, whereas standard gravity is dominant at small scales. As a consequence, there exists a \emph{point} where the effects are counterbalanced,…
Among all metrics on $\mathbb S^d$ with $d>4$ that are conformal to the standard metric and have positive scalar curvature, the total $\sigma_2$-curvature, normalized by the volume, is uniquely (up to M\"obius transformations) minimized by…
The radial motion of a self-graviting charged dust and stability condition of the static charged dust spheres are considered. The stability is possible for the bound states of the weakly charged layer with abnormal charge with respect to…
We review recent results regarding the problem of the stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds. We shall describe techniques and methods from smooth and non-smooth geometry, the fruitful…
Llarull's Theorem states that any Riemannian metric on the $n$-sphere which has scalar curv{\-}ature greater than or equal to $n(n-1)$, and whose distance function is bounded below by the unit sphere's, is isometric to the unit sphere.…
Using elementary number theory, we prove several results about the complexity of CR mappings between spheres. It is known that CR mappings between spheres, invariant under finite groups, lead to sharp bounds for degree estimates on real…
The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of…
In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…
We investigated the boundary between stable and unstable regimes of accretion and its dependence on different parameters. Simulations were performed using a "cubed sphere" code with high grid resolution (244 grid points in the azimuthal…
Two drastically different theories predict the marginal criticality of jamming. The full replica symmetry breaking (fullRSB) theory [1-4] predicts the power-law distributions of weak contact forces and small inter-particle gaps in…
We prove a quantitative rigidity result for almost constant mean curvature spheres in $\mathbb{R}^3$. Under a sub--two--sphere Willmore bound and a small $L^2$--CMC defect, we show that an almost--CMC surface is close to the round sphere,…
The investigation of gravity in higher-dimensional spacetime has transitioned from a mathematical curiosity to a fundamental framework in theoretical physics, catalyzed by the dimensional requirements of String theory and M-theory. In this…
It is a famous result of relativistic stellar structure that (under mild technical conditions) a static fluid sphere satisfies the Buchdahl--Bondi bound 2M/R <= 8/9; the surprise here being that the bound is not 2M/R <= 1. In this article…
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…
We prove Llarull-type rigidity for $S^{n-m}\times\mathbb{T}^m$ ($3\le n\le 7$, $1\le m\le n-2$). If a closed spin $(M^n,g)$ admits a degree-nonzero map to $S^{n-m}\times\mathbb{T}^m$ whose spherical projection is area non-increasing, and…
The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in…
A modified three-dimensional mean spherical model with a L-layer film geometry under Neumann-Neumann boundary conditions is considered. Two spherical fields are present in the model: a surface one fixes the mean square value of the spins at…
Determination of the proton charge radius by different methods has produced an inconsistency. The most precise value (from spectroscopy of muonic hydrogen) strongly disagrees with three less accurate values (from spectroscopy of ordinary…
We give sharp limiting case Hardy inequalities on the sphere $\mathbb{S}^{2}$ and show that their optimal constants are unattainable by any $f\in H^{1}\left(\mathbb{S}^{2}\right)\setminus\{0\}$. The singularity of the problem is related to…
We produce the simple formula for the radius R of a cold body of mass M, (4 pi rho/3)^{1/3} R = I.M^{1/3} / [1+ (M/Mp)^{2/3}], where I is one for white dwarfs with non-relativistic electrons, but depends on the ratio of the total mass to…