Related papers: A double large deviation principle for monge-amper…
We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.
We consider the motion of a massive particle in a static, weakly-curved spacetime where the gravitational field is taken to be quantized. We find that Newton's law of free-fall is modified by quantum-gravitational corrections, in addition…
Massive gravity can be described by adding to the Einstein-Hilbert action a function V of metric components. By using the Hamiltonian canonical analysis, we find the most general form of V such that five degrees of freedom propagate non…
We establish a large deviation principle for the process of the largest eigenvalue of an Hermitian Brownian motion. By a contraction principle, we recover the LDP for the largest eigenvalue of a rank one deformation of the GUE.
We give a new proof for the interior regularity of strictly convex solutions of the Monge-Amp\`ere equation. Our approach uses a doubling inequality for the Hessian in terms of the extrinsic distance function on the maximal Lagrangian…
We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak…
Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics.…
Modified Newtonian Dynamics (MOND) is an alternative to the dark matter hypothesis that attempts to explain the "missing gravity" problem in astrophysics and cosmology through a modification to objects' dynamics. Since its conception in…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…
We present a concise description of the basic features of gravity-matter models based on the formalism of non-canonical spacetime volume-forms in its two versions: the method of non-Riemannian volume-forms (metric-independent covariant…
We consider the gravitational potential and the gravitational rotation field generated by an spherical mass distribution with exponential density, when the force between any two mass elements is not the usual Newtonian one, but some general…
We propose a new point of view for interpreting Newton's and Einstein's theories of gravity. By taking inspiration from Continuum Mechanics and its treatment of anisotropies, we formulate new gravitational actions for modified theories of…
The main principle of affine quantum gravity is the strict positivity of the matrix \{\hat g_{ab}(x)\} composed of the spatial components of the local metric operator. Canonical commutation relations are incompatible with this principle,…
We examine the implications of Modified Newtonian Dynamics (MOND) on the large scale structure in a Friedmann-Robertson-Walker universe. We employ a ``Jeans swindle'' to write a MOND-type relationship between the fluctuations in the density…
Recent conjectures that there are mesoscopically ``large'' extra dimensions, through which gravity propagates have interesting implications for much of physics. The scenario implies gross departures from Newton's law of gravity at small…
In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Amp\`ere type equations. We prove that the strong maximum principle holds at points where the function is strictly convex but not necessarily…
The vacuum catastrophe is a fundamental puzzle, where the observed scales of the cosmological constant are many orders of magnitude smaller than the natural scales expected in the theory. This work proposes a new "bi-world" construction…
We revisit the classical monotone-follower problem and consider it in a generalized formulation. Our approach is based on a compactness substitute for nondecreasing processes, the Meyer-Zheng weak convergence, and the maximum principle of…
We prove a comparison principle for the pluripotential complex Monge-Amp\`ere flows for the right-hand side of the form $dt \wedge d\mu$ where $d\mu$ is dominated by a Monge-Amp\`ere measure of a bounded plurisubharmonic function. As a…