Related papers: A Variational Scalar Conformal Flow for Lorentz-Co…
We construct a particular flow in the space of 2D Euclidean QFTs on a torus, which we argue is dual to a class of solutions in 3D Euclidean gravity with conformal boundary conditions. This new flow comes from a Legendre transform of the…
In recent work of Chan-Huang-Lee, it is shown that if a manifold enjoys uniform bounds on (a) the negative part of the scalar curvature, (b) the local entropy, and (c) volume ratios up to a fixed scale, then there exists a Ricci flow for…
The inverse cascade in two-dimensional hydrodynamic turbulence exhibits a mysterious phenomenon. Numerical simulations have shown that the nodal isolines of certain scalars actively transported in the flow (eg, the vorticity in…
We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into…
We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the…
A Dalitz plot analysis of the OZI rule violating decay $D^+_s$ into $\pi^- \pi^+ \pi^+$ is presented using different partial wave approaches. Scalar and vector waves are described by $K$-matrices; their production is parameterized in a…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
We present a synthetic notion of scalar curvature (and its integral) for Riemannian manifolds and metric measure spaces, defined in terms of the initial slope of a Gaussian (double) integral. We explicitly calculate the integral scalar…
We define rigorously a solution to the fourth-order total variation flow equation in $\mathbb{R}^n$. If $n\geq3$, it can be understood as a gradient flow of the total variation energy in $D^{-1}$, the dual space of $D^1_0$, which is the…
We review the classical and quantum mechanics of Stueckelberg, and introduce the compensation fields necessary for the gauge covariance of the Stueckelberg- Schr\"odinger equation. To achieve this, one must introduce a fifth, Lorentz…
The Renormalization Group Flow Equations of the Scalar-QED model near Planck's scale are computed within the framework of the average effective action. Exact Flow Equations, corrected by Einstein Gravity, for the running self-interacting…
We employ three different methods to prove the following result on prescribed scalar curvature plus mean curvature problem: Let $(M^n,g_0)$ be a $n$-dimensional smooth compact manifold with boundary, where $n \geq 3$, assume the conformal…
The motion of rarefied gases for uniform shear flow at the kinetic level is governed by the spatially homogeneous Boltzmann equation with a deformation force. In the paper we study the corresponding Cauchy problem with initial data of…
We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent $\sigma \in (1/2,1)$. This extends the result of Chen-Xu (Invent. Math.…
We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P,…
The inflation-free solution of problems of the modern cosmology (horizon, cosmic initial data, Planck era, arrow of time, singularity,homogeneity, and so on) is considered in the conformal-invariant unified theory given in the space with…
Conformable derivatives provide a fractional-looking calculus that remains local and admits a simple representation through classical derivatives with explicit weights. In this paper we develop a systematic operator-theoretic perspective…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
Einstein's theory of general relativity is written in terms of the variables obtained from a conformal--traceless decomposition of the spatial metric and extrinsic curvature. The determinant of the conformal metric is not restricted, so the…
A one-parameter family of coupled flows depending on a parameter $\kappa>0$ is introduced which reduces when $\kappa=1$ to the coupled flow of a metric $\omega$ with a $(1,1)$-form $\alpha$ due recently to Y. Li, Y. Yuan, and Y. Zhang. It…