Related papers: Weighted Chui's conjecture
The recent proof of the sharp weighted bound for Calder\'on-Zygmund operators has led to much investigation in sharp mixed bounds for operators and commutators, that is, a sharp weighted bound that is a product of at least two different…
We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.
In this paper we take up the quantal two-centre problem where the Coulomb centres have arbitrary positive charges. In analogy with the symmetric case, treated in the second paper of this series of papers, we use the knowledge on the…
We establish a version, formulated in terms of non-Archimedean pluripotential theory, of the Yau-Tian-Donaldson conjecture for constant scalar curvature and, more generally, weighted extremal K\"ahler metrics with prescribed compact…
In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower…
The general formula for the interaction potential between two point electric charges which contains the lowest order corrections to the vacuum polarization is derived and investigated. Analytical derivation of this formula is based on the…
We prove the following comparison theorem for metrics with nonnegative scalar curvature, also known as the dihedral rigidity conjecture by Gromov: for $n\le 7$, if an $n$-dimensional prism has nonnegative scalar curvature and weakly mean…
We study Riemannian manifolds with boundary under a lower $N$-weighted Ricci curvature bound for $N$ at most $1$, and under a lower weighted mean curvature bound for the boundary. We examine rigidity phenomena in such manifolds with…
The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to balls.
The goal of this article is to discuss a recent conjecture of the two authors, which aims to describe the long time behavior of solutions to one-dimensional dispersive equations with cubic and higher nonlinearities. These problems arguably…
We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…
We show that topological 3D gravity with torsion can be formulated as a Chern-Simons gauge theory, provided a specific parameter, known as the effective cosmological constant, is negative. In that case, the boundary dynamics of the theory…
This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary…
We formulate a relative analogue of the Clemens conjectures for 1/2-log Calabi-Yau threefold pairs (X,Y) (where K_X+2Y is isomorphic to O_X). This framework rests on the restoration of a perfect deformation/obstruction duality specific to…
We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We conjecture an intrinsic UV cutoff for the validity of the effective field theory with a large number of species coupled to gravity. In four dimensions such a UV cutoff takes the form $\Lambda=\sqrt{\lambda/ N}M_p$ for $N$ scalar fields…
In this article, we extend the example constructed in the paper by Sormani-Tian-Wang to build new examples that satisfy the assumptions of the conjecture by Gromov. Each of these new examples of sequence converges to a limit space with…
We study Q-balls associated with local U(1) symmetries. Such Q-balls are expected to become unstable for large values of their charge because of the repulsion mediated by the gauge force. We consider the possibility that the repulsion is…
In this paper, we investigate universal estimates for eigenvalues of a buckling problem. For a bounded domain in a Euclidean space, we give a positive contribution for obtaining a sharp universal inequality for eigenvalues of the buckling…