Related papers: On the timelike Liouville three-point function
We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for…
Toda Conformal Field Theories (CFTs) form a family of two-dimensional CFTs indexed by semisimple and complex Lie algebras. One of their remarkable features is that they are natural generalizations of Liouville CFT that enjoy an enhanced…
In this paper, a new notion, named Riemann-Liouville fractional cosine function is presented. It is proved that a Riemann-Liouville $\alpha$-order fractional cosine function is equivalent to Riemann-Liouville $\alpha$-order fractional…
The path integral description of the Wess-Zumino-Witten $\to$ Liouville reduction is formulated in a manner that exhibits the conformal invariance explicitly at each stage of the reduction process. The description requires a conformally…
We analyse the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the Kahler formalism, we extract the coefficient of the leading divergence in $\sim A\Lambda^2 (\ln…
Three concepts of local times for deterministic c{\`a}dl{\`a}g paths are developed and the corresponding pathwise Tanaka--Meyer formulae are provided. For semimartingales, it is shown that their sample paths a.s. satisfy all three pathwise…
It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above…
We propose a new heuristic approach to integral moments of L-functions over function fields, which we demonstrate in the case of Dirichlet characters ramified at one place (the function field analogue of the moments of the Riemann zeta…
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems. Assume that $p=2q+3>1$ is…
A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the…
We establish the unique solvability of solutions in Sobolev spaces to linear parabolic equations in a more general form than those in the literature. A distinguishing feature of our equations is the inclusion of a half-order time derivative…
Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an It\^{o}…
We review both the construction of conformal blocks in quantum Liouville theory and the quantization of Teichm\"uller spaces as developed by Kashaev, Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert space acted on…
It is well known that second order homogeneous linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation underlies the Liouville-Green method and many other techniques for…
The fundamental concept of phase space for particles moving in the four-dimensional spacetime is analyzed. Particle distribution density is defined as differential form, which degree may be different in various cases. It should be…
The Coulomb gauge has at least two advantadges over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop…
A Liouville classification of a natural Hamiltonian system on the projective plane with a rotation metric and a linear integral is obtained. All Fomenko--Zieschang invariants (i.e., labeled molecules) of the system are calculated.
We study a class of solutions to the SL(2,R)_k Knizhnik-Zamolodchikov equation. First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional Anti-de Sitter space…
We consider timelike Liouville theory with FZZT-like boundary conditions. The bulk one-point and boundary two-point structure constants on a disk are derived using bootstrap. We find that these structure constants are not the analytic…
We give applications of known and new Liouville type theorems to universal singularity and decay estimates for non scale invariant elliptic problems, including Lane-Emden and Schr\"odinger type systems. This applies to various classes of…