Related papers: On an extremal problem in two Siegel domains

We give a new derivation of the distance-dependent two-point function of planar quadrangulations by solving a new direct recursion relation for the associated slice generating functions. Our approach for both the derivation and the solution…

We develop the Perron-Wiener-Brelot method of solving the Dirichlet problem at the Martin boundary of a fine domain in $\RR^n$ ($n\ge2$).

We introduce a new class of discrete approximations of planar domains that we call "hedgehog domains". In particular, this class of approximations contains two-step Aztec diamonds and similar shapes. We show that fluctuations of the height…

We prove local pointwise second derivative estimates for positive $W^{2,p}$ solutions to the $\sigma_k$-Yamabe equation on Euclidean domains, addressing both the positive and negative cases. Generalisations for augmented Hessian equations…

We give the presentation of exceptional bounded symmetric domains using the Albert algebra and exceptional Jordan triple systems. The first chapter is devoted to Cayley-Graves algebras, the second to exceptional Jordan triple systems. In…

The fundamental gap is the difference between the first two Dirichlet eigenvalues of a Schr\"odinger operator (and the Laplacian, in particular). For horoconvex domains in hyperbolic space, Nguyen, Stancu and Wei conjectured that it is…

We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…

We discuss the problem where the extremal function in embedding theorem of some (generally speaking, non-integer) order is the constant function. We obtain the necessary and sufficient conditions of this.

We show that the there exists an algebraic rate of convergence of solutions of finite-difference approximations for uniformly elliptic Isaacs in smooth bounded domains.

We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…

We prove the so-called second case of the fractional Korn inequality for uniform domains. We obtain this result as an application of a novel fractional Korn-type inequality formulated in terms of truncated seminorms, which turns out to be…

The intention of this survey to collect in one paper many recent results and advances related with Bergman type projection acting in various spaces of analytic functions in several complex variables in the unit ball, tubular domains over…

We prove a number of results on the geometry associated to the solutions of evolution equations given by first-order differential operators on manifolds. In particular, we consider distance functions associated to a first-order operator,…

Let $F$ be a Hecke-Maa\ss\ cusp form for $\mathrm{SL}(3,\mathbb{Z})$. We obtain the first non-trivial upper bound of the second moment of $L(F,s)$ in $t$-aspect: $$\int_{T}^{2T}|L(F,1/2+it)|^2 dt\ll_{F,\varepsilon}…

In this paper, we study the extremal problem for the Strichartz inequality for the Schr\"{o}dinger equation on $\mathbb{R}^2$. We show that the solutions to the associated Euler-Lagrange equation are exponentially decaying in the Fourier…

We obtain an explicit integral representation of Siegel-Whittaker functions on Sp(2,R) for the large discrete series representations. We have another integral expression different from that of Miyazaki [7].

In this note we extend to arbitrary dimensions a couple of results due respectively to Mattei-Moussu and to Camara-Scardua in dimension 2. We also provide examples of singular foliations having a Siegel-type singularity and answering in the…

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.

We study the lattice point problem associated with a special class of high-dimensional finite type domains via estimating the Fourier transforms of corresponding indicator functions.

We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H2 of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and…