Related papers: A note on arclength null quadrature domains

Exceptional domains are domains on which there exists a positive harmonic function, zero on the boundary and such that the normal derivative on the boundary is constant. Recent results classify exceptional domains as belonging to either a…

An infinite structure has the finite length property (over a given field) if, for each of its finite powers, chains of equivariant subspaces in the corresponding free vector space are bounded in length. Prior work showed that the countable…

This note is intended to explain the proof of two facts about quadrature domains: first, they are essentially unique if they exist; and second, they do exist for a large class of weight functions. The proofs roughly follow Sakai's…

This paper studies plane domains satisfying a quadrature identity with respect to the singular weight $\rho_0(w)=|w|^{-2}$. These are referred to as log-weighted quadrature domains (LQDs). The logarithmic singularity at $w=0$ leads to…

We address the problem of topology of quadrature domains, namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity.

In this paper we study general conditions to prove the infiniteness of the genus of certain towers of function fields over a perfect field. We show that many known examples of towers with infinite genus are particular cases of these…

The purpose of this paper is to characterize the zero sets of holomorphic functions in the Nevanlinna class on a class of convex domains of infinite type in $\mathbb{C}^2$. Moreover, we also obtain $L^p$ estimates, $1 \leq p \leq \infty$,…

In the late ten years, the resolution of the equation $\bar\partial u=f$ with sharp estimates has been intensively studied for convex domains of finite type by many authors. In this paper, we consider the case of lineally convex domains. As…

We discuss without proof some recent advances in the theory of distributional boundary values, and give an example to show that the condition that a piecewise smooth domain has generic corners is necessary for the existence of boundary…

We develop a novel topological framework that yields results constraining the distribution of zeros of certain zero mean real-valued maps, namely those obtained from composing a fixed equivariant map with linear functionals. We use this…

Let X be a compact Kahler manifold with negative sectional curvature and residually finite fundamental group. Then its universal covering is a bounded domain in an affine space.

We investigate the birational section conjecture for curves over function fields of characteristic zero and prove that the conjecture holds over finitely generated fields over Q if it holds over number fields.

We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras…

For a transcendental entire function, a partial affirmative answer to Baker's question on the boundedness of its Fatou components is given. In addition, we have addressed Wang's question on Fej\'er gaps. Certain results about functions with…

In this paper we establish three results on small-height zeros of quadratic polynomials over $\overline{\mathbb Q}$. For a single quadratic form in $N \geq 2$ variables on a subspace of $\overline{\mathbb Q}^N$, we prove an upper bound on…

We consider the zeros on the boundary $\partial \Omega$ of a Neumann eigenfunction $\phi_{\lambda}$ of a real analytic plane domain $\Omega$. We prove that the number of its boundary zeros is $O (\lambda)$ where $-\Delta \phi_{\lambda} =…

We prove new results on the existence, non-existence, localization and multiplicity of nontrivial radial solutions of a system of elliptic boundary value problems on exterior domains subject to nonlocal, nonlinear, functional boundary…

It has been well known for a long time that the height function of random lozenge tilings of large domains follow a law of large number and possible limits called dimer limit shapes are well understood. For the next order, it is expected…

Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of…

It is an open problem in general to prove that there exists a sequence of $\Delta_g$-eigenfunctions $\phi_{j_k}$ on a Riemannian manifold $(M, g)$ for which the number $N(\phi_{j_k}) $ of nodal domains tends to infinity with the eigenvalue.…