相关论文: On $n$-superharmonic functions and some geometric …
Complex-valued functions defined on a finite interval $[a,b]$ generalizing power functions of the type $(x-x_0)^n$ for $n\geq 0$ are studied. These functions called $\Phi$-generalized powers, $\Phi$ being a given nonzero complex-valued…
In this article we extend B. Simon's construction and results for leading order eigenvalue asymptotics to $n$-dimensional Schr\"odinger operators with non-confining potentials given by: $H^\alpha_n=-\Delta +\prod\limits_{i=1}^n…
We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our…
We introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them. This concept contains as a special case several similar concepts which have been considered e.g. by Arnold and…
We study hyperbolic mappings depending on a parameter $\varepsilon $. Each of them has an invariant Cantor set. As $\varepsilon $ tends to zero, the mapping approaches the boundary of hyperbolicity. We analyze the asymptotics of the gap…
This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous odd…
The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy…
In this note we investigate the behavior of harmonic functions at singular points of $\mathsf{RCD}(K,N)$ spaces. In particular we show that their gradient vanishes at all points where the tangent cone is isometric to a cone over a metric…
We investigate Stein-Malliavin approximations for nonlinear functionals of geometric interest of Gaussian random eigenfunctions on the unit $d$ -dimensional sphere ${\mathbb{S}}^{d},$ $d\geq 2.$ All our results are established in the high…
Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties convergence results for sequences of distribution functions \phi_n=|s_N| / |s_N|_{L^2} for sections s_N\in…
Andrews-Dyson-Hickerson, Cohen build a striking relation between q-hypergeometric series, real quadratic fields, and Maass forms. Thanks to the works of Lewis-Zagier and Zwegers we have a complete understanding on the part of these…
We explore Liouville's theorem and the Strong Liouville Property (SLP) for harmonic functions on Riemannian cones and surfaces. Our approach recasts the classical Liouville property in terms of the growth of radial eigenfunctions (in the…
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+\epsilon\lambda,b;c+\lambda;x),\qquad 0<x<1\] as $\lambda\to+\infty$ in the neigbourhood of $\epsilon x=1$ when the parameter $\epsilon>1$ and…
We show exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under finite first moment condition, and establish the dimension formula by the entropy over the drift. We also treat the…
We derive an asymptotic error formula for Gauss--Legendre quadrature applied to functions with limited regularity, using the contour-integral representation of the remainder term. To address the absence of uniformly valid approximations of…
In this article, we extend the results of both Shao and Holzegel-Shao to the AdS-Einstein-Maxwell system $({M}, g, F)$. We study the asymptotics of the metric $g$ and the Maxwell field $F$ near the conformal boundary ${I}$ for the fully…
We consider (2+1)-dimensional (N, M)-extended higher-spin anti-de Sitter supergravity and study its asymptotic symmetries. The theory is described by the Chern-Simons action based on a real, infinite-dimensional higher-spin superalgebra. We…
We study the 3-point functions of gauge-invariant scalar operators in four dimensional $\mathcal{N}=2$ superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of…
We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1<p<\infty$, following the scheme described in Manfredi et al. (2009) for the Euclidean case. The new tool that allows us…
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…