Related papers: Polyakov conjecture for hyperbolic singularities

We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

In the first part of this article, we complete the program announced in the preliminary note [8] by proving a conjecture presented in [9] that states the equivalence of contractibility and p_{1}-stability for generalized spaces of formal…

We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.

A new computational method to solve the hyperbolic (Vlasov) equation and the elliptic (Poisson-like) equation at the polar axis is proposed. It is shown that the value of a scalar function at the polar axis can be predicted by its…

We prove some Liouville theorems for the stationary Navier-Stokes system for incompressible fluids. We provide some sufficient conditions on the low frequency part of the solution, using some properties of classical singular integrals with…

The examples are considered of integrable hyperbolic equations of third order with two independent variables. In particular, an equation is found which admits as evolutionary symmetries the Krichever--Novikov equation and the modified…

We classify polar actions on complex hyperbolic spaces up to orbit equivalence.

We construct self-adjoint Laplacians and symmetric Markov semigroups on partially hyperbolic attractors and on hyperbolic attractors with singularities, endowed with Gibbs u-measures. If the measure has full support, we can also guarantee…

We establish a Liouville type theorem for fully nonlinear uniformly elliptic equations in exterior domains in half spaces under quadratic boundary data and a quadratic growth condition, that is, any viscosity solution tends to a quadratic…

We prove new (sharp) Liouville-type properties via degenerate Hadamard three-sphere theorems for fully nonlinear equations structured over Heisenberg vector fields. As model examples, we cover the case of Pucci's extremal operators…

Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess nontrivial entire solutions) guarantee optimal universal estimates of solutions of related initial and…

Liouville systems on Riemann surfaces are instrumental in modeling species growth and particle dynamics in biology and physics. Previously, we established a priori estimates for parameters across regions defined by critical hyper-surfaces.…

Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and…

We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree $d \ge 2$ polynomials. Our metric is constructed by considering the measure-theoretic entropy of a polynomial with respect to some equilibrium…

An alternative method is described for determining the hyperbolic structure on a link complement, and some of its elementary consequences are examined. The method is particularly suited to alternating links.

The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is…

We obtain nonperturbative results in the framework of continuous Liouville theory. In particular, we express the specific heat ${\cal Z}$ of pure gravity in terms of an expansion of integrals on moduli spaces of punctured Riemann spheres.…

We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to $L^q$ with $q \in [2,\infty)$, we prove a pointwise asymptotic…

We establish various results concerning the uniqueness of zero velocity solutions for the static barotropic Navier--Stokes system. Some of them can be seen as Liouville-type theorems for problems in unbounded physical space.