Cut Locus on Compact Manifolds and Uniform Semiconcavity Estimates for a Variational Inequality

The logarithmic HLS inequality for systems on compact manifolds

Gradient estimates for eigenfunctions on compact Riemannian manifolds with boundary

The purpose of this paper is to prove the L∞ gradient estimates and L∞ gradient estimates for the unit spectral projection operators of the Dirichlet Laplacian and Neumann (or more general, Ψ1-Robin) Laplacian on compact Riemannian manifolds (M, g) of dimension n ≥ 2 with C2 boundary . And we also get an upper bounds for normal derivatives of the unit spectral projection operators of the Dirich...

A Variational Approach for Compact Homogeneous Einstein Manifolds

Einstein metrics of volume 1 on a closed manifold can be characterized variationally as the critical points of the Hilbert action [Hi], which associates to each Riemannian metric of volume 1 the integral of its scalar curvature. As is well-known, the gradient vector of the Hilbert action with respect to the natural L2 metric is precisely the negative of the traceless Ricci tensor. Consequently,...

A Berger-green Type Inequality for Compact Lorentzian Manifolds

We give a Lorentzian metric on the null congruence associated with a timelike conformal vector field. A Liouville type theorem is proved and a boundedness for the volume of the null congruence, analogous to a well-known Berger-Green theorem in the Riemannian case, will be derived by studying conjugate points along null geodesics. As a consequence, several classification results on certain compa...

Uniform Convergence to a Left Invariance on Weakly Compact Subsets

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...