Related papers: Rigidity in the Positive Mass Theorem with Charge
In this paper, we study the well-posedness of Poisson-Nernst-Planck system with no-flux boundary condition and singular permanent charges in two dimension. The main difficulty comes from the lack of integrability of singular permanent…
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity.…
We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green's function. The theorem also holds if the conformal Green's function is replaced…
We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the assumption that the rotation in the basis satisfies a Diophantine condition. We prove…
The soft photon theorem, in its standard form, requires corrections when the asymptotic particle states carry magnetic charges. These corrections are deduced using electromagnetic duality and the resulting soft formula conjectured to be…
We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient that it is radially bounded, i.e. that every ray passing through one of its elements…
Complete constraint analysis and choice of gauge conditions consistent with equations of motion is done for Abelian Chern Simons field interacting minimally with a complex scalar field. The Dirac-Schwinger consistency condition is satisfied…
Gauge fixing may be done in different ways. We show that using the chain structure to describe a constrained system, enables us to use either a perfect gauge, in which all gauged degrees of freedom are determined; or an imperfect gauge, in…
In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the…
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…
We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions…
A recently proposed theory of modified gravity with an explicit ``anomalous'' coupling of the Ricci curvature to matter is discussed, and an inequality is derived which expresses a necessary and sufficient condition to avoid the notorius…
In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion.…
We investigate the mapping of Dirac gaugino masses through regions of strong coupling, focussing on SQCD with an adjoint. These models have a well-known Kutasov duality, under which a weakly coupled electric UV description can flow to a…
We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$…
The present theory is closely related to Dirac's equation of the electron, but not to his magnetic monopole theory, except for his relation between electric and magnetic charge. The theory is based on the fact, that the massless Dirac…
We study the $(1+1)$ dimensional generalized Dirac oscillator with a position-dependent mass. In particular, bound states with zero energy as well as non zero energy have been obtained for suitable choices of the mass function/oscillator…
In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.
The weak gravity conjecture suggests that, in a self-consistent theory of quantum gravity, the strength of gravity is bounded from above by the strengths of the various gauge forces in the theory. In particular, this intriguing conjecture…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…