Related papers: Bounds for canonical Green's function at cusps

In this paper, we obtain a unified characterization of uniformly rectifiable sets of {\it any codimension} in terms of a Carleson estimate on the second derivatives of the Green function. When restricted to domains with boundaries of…

We introduce a notion of relative isospectrality for surfaces with boundary having possibly non-compact ends either conformally compact or asymptotic to cusps. We obtain a compactness result for such families via a conformal surgery that…

We produce an upper bound for the Hausdorff dimension of the graph of a Weierstrass-type function. Whilst strictly weaker than existing results, it has the advantage of being directly computable from the theory of hyperbolic iterated…

In this paper, new sharp bounds for circular functions are proved. We provide some improvements of previous results by using infinite products, power series expansions and a generalisation of the so-called Bernoulli inequality. New proofs,…

We prove the existence of Cannon-Thurston maps for Kleinian groups corresponding to pared manifolds whose boundary is incompressible away from cusps. We also describe the structure of these maps in terms of ending laminations.

We show that the infimum of the dual volume of the convex core of a convex co-compact hyperbolic $3$-manifold with incompressible boundary coincides with the infimum of the Riemannian volume of its convex core, as we vary the geometry by…

The paper considers a global version of the notion of log canonical threshold for plurisubharmonic functions $u$ of logarithmic growth in $\mathbb{C}^n$, aiming at description of the range of all $p>0$ such that $e^{-u}\in…

It is known that a closed collapsed Riemannian $n$-manifold $(M,g)$ of bounded Ricci curvature and Reifenberg local covering geometry admits a nilpotent structure in the sense of Cheeger-Fukaya-Gromov with respect to a smoothed metric…

We present a refined Green's function estimate of the time measurable parabolic operators on conic domains that involves mixed weights consisting of appropriate powers of the distance to the vertex and of the distance to the boundary.

We apply the method of two-point quasiclassical Green's function to geometries where the trajectories include interfering paths and loops. For a system of two superconducting layers separated by partially transparent interface, corrections…

We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Teorem: any special scroll is the projection of a canonical scroll and…

We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image. Furthermore, any spherical metric on the torus with cone singularities of negative curvature and all closed…

We study the existence of the Green function for an elliptic system in divergence form $-\nabla\cdot a\nabla$ in $\mathbb{R}^d$, with $d>2$. The tensor field $a=a(x)$ is only assumed to be bounded and $\lambda$-coercive. For almost every…

In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…

The goal of this work is to give new quantitative results about the distribution of semi-arithmetic hyperbolic surfaces in the moduli space of closed hyperbolic surfaces. We show that two coverings of genus $g$ of a fixed arithmetic surface…

We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine…

In this paper we describe a method for computing a basis for the space of weight $2$ cusp forms invariant under a non-split Cartan subgroup of prime level $p$. As an application we compute, for certain small values of $p$, explicit…

Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these…

In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a…

In this paper, we consider a linear fractional differential equation with fractional boundary conditions. First, by obtaining Green's function, we derive the Lyapunov-type inequalities for such boundary value problems. Furthermore, we use…