相关论文: Some inequalities between Ahlfors regular conforma…
We review a selection of the literature on the distortion of metric notions of dimension under quasiconformal, quasisymmetric, and Sobolev mappings. Our story begins with Gehring's landmark 1973 higher integrability theorem for…
A resistance network is a connected graph $(G,c)$. The conductance function $c_{xy}$ weights the edges, which are then interpreted as conductors of possibly varying strengths. The Dirichlet energy form $\mathcal E$ produces a Hilbert space…
The obstruction for a perturbative reconstruction of the five-dimensional bulk metric starting from the four-dimensional metric at the boundary,that is, the Dirichlet problem, is computed in dimensions $6\leq d\leq 10$ and some comments are…
Resistance in standard conductors decreases with increasing cross-section. Yet, in low-dimensional superconductors and superfluids residual resistance arises from topological fluctuations of the order parameter manifesting as phase slips in…
We investigate the superradiant instability for a charged scalar field in a $D$-dimensional small Reissner-Nordstr\"om-Anti-de Sitter (RN-AdS) black hole. Firstly, we solve the charged Klein-Gordon equation analytically by a matching…
The Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric components depend on the radial coordinate r and [D/2] latitude variables \mu_i that are subject to the constraint \sum_i \mu_i^2=1. We find a coordinate…
We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpi\'{n}ski gaskets and each of which is equipped with a canonical strongly local regular symmetric Dirichlet form. We prove that any…
The purpose of this note is to characterize the asymptotic dimension $asdim(X)$ of metric spaces $X$ in terms similar to Property A of Yu: If $(X,d)$ is a metric space and $n\ge 0$, then the following conditions are equivalent: [a.]…
Given a sequence of Hermitian holomorphic line bundles $(L_k,h_k)$ over a complex manifold $M$ which may not be compact, we generalize the scaling method in arXiv:2310.08048 to study the asymptotic behavior of the Bergman kernels and…
Wavelet bases and frames consisting of band limited functions of nearly exponential localization on Rd are a powerful tool in harmonic analysis by making various spaces of functions and distributions more accessible for study and…
We construct a conservative and strongly local regular symmetric Dirichlet form on the pointed Gromov--Hausdorff limit space and demonstrate the stability of heat kernel estimates under this convergence. Furthermore, we establish the Mosco…
The issue related to the so-called dimensional reduction procedure is revisited within the Euclidean formalism. First, it is shown that for symmetric spaces, the local exact heat-kernel density is equal to the reduced one, once the harmonic…
Let $d \geq 2$, $\alpha \in (0,2)$, and $X$ be the rectilinear $\alpha$-stable process on $\mathbb{R}^d$. We first present a geometric characterization of an open subset $D\subset \mathbb{R}^d$ so that the part process $X^D$ of $X$ in $D$…
We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of Jones (Acta Math. 1981) states that uniform domains in…
Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a…
We derive some necessary conditions on a Riemannian metric $(M, g)$ in four dimensions for it to be locally conformal to K\"ahler. If the conformal curvature is non anti--self--dual, the self--dual Weyl spinor must be of algebraic type $D$…
We consider minimisers of the $p$-exponential conformal energy for homeomorphisms $f:R \to S$ of finite distortion $\IK(z,f)$ between analytically finite Riemann surfaces in a fixed homotopy class $[f_0]$,\[ \mE_p(f:R,S)=\int_R…
We investigate the quasinormal spectrum of electromagnetic perturbations of rotating black strings. Among the solutions of Einstein equations in the presence of a negative cosmological constant there are asymptotically anti-de Sitter (AdS)…
We provide a new definition of a local walk dimension $\beta$ that depends only on the metric and not on the existence of a particular regular Dirichlet form or heat kernel asymptotics. Moreover, we study the local Hausdorff dimension…
The holographic duality (also known as AdS/CFT correspondence or gauge/gravity duality) postulates that strongly coupled quantum field theories can be described in a dual way in asymptotically Anti-de Sitter space. One of the cornerstones…