相关论文: Shape Theorems for Poisson Hail on a Bivariate Gro…

I show that the evolution of a two dimensional surface in a Laplacian field can be described by Hamiltonian dynamics. First the growing region is mapped conformally to the interior of the unit circle, creating in the process a set of…

We study a hairy black hole solution in the dilatonic Einstein-Gauss-Bonnet theory of gravitation, in which the Gauss-Bonnet term is non-minimally coupled to the dilaton field. Hairy black holes with spherical symmetry seem to be easily…

Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in…

This paper is concerned with the study of a class of nonsmooth cost functions subject to a quasi-linear PDE in Lipschitz domains in dimension two. We derive the Eulerian semi-derivative of the cost function by employing the averaged adjoint…

We consider the global evolution problem for Einstein's field equations in the near-Minkowski regime and study the long-time dynamics of a massive scalar field evolving under its own gravitational field. We establish the existence of a…

It has recently been revealed that spinning black holes of the photon-fluid model can support acoustic `clouds', stationary density fluctuations whose spatially regular radial eigenfunctions are determined by the $(2+1)$-dimensional…

Hall magnetohydrodynamics (MHD) properties near a two-dimensional (2D) X-type magnetic neutral line in the steady state are considered via heuristic and rigorous developments. Upon considering the steady-state as the asymptotic limit of the…

We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…

A Poisson outdegree-one graph is an oriented graph based on a Poisson point process such that each vertex has only one outgoing edge. The paper focuses on the absence of percolation for such graphs. Our main result is based on two…

It is proved that on nilmanifolds with abelian complex structure, there exists a canonically constructed non-trivial holomorphic Poisson structure. We identify the necessary and sufficient condition for its associated cohomology to be…

We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…

In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results…

In the present work, it is shown that an asymptotically flat spherical black hole can have a nontrivial signature of any field for an exterior observer if the energy momentum tensor of the corresponding field is either tracefree or if the…

We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…

In a recent paper by the authors, growth properties of the Fourier transform on Euclidean space and the Helgason Fourier transform on rank one symmetric spaces of non-compact type were proved and expressed in terms of of a modulus of…

The dynamical evolution of the Hajicek $1$-form is derived in Einstein-Cartan (EC) theory. We find that like Einstein theory of gravity, the evolution equation is related to a projected part of the Einstein tensor $(\hat{G}_{ab})$ on a…

Thermodynamics of scalar fields is investigated in three dimensional black hole backgrounds in two approaches. One is mode expansion and direct computation of the partition sum, and the other is the Euclidean path integral approach. We…

In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…

We make use of the fact that the optical geometry near a static non-degenerate Killing horizon is asymptotically hyperbolic to investigate universal features of black hole physics. We show how the Gauss-Bonnet theorem allows certain lensing…

$p$-form electrodynamics in $d\geq 2$ dimensions is shown to emerge as the edge modes of a topological field theory with a precise set of boundary conditions, through the Hamiltonian reduction of its action. Electric and magnetic charges…