相关论文: Curvature of basis exchange walks

We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic…

We are concerned with the study of different notions of curvature on graphs. We show that if a graph has stronger inner-outer curvature growth than a model graph, then it has faster volume growth too. We also study the relationhips of…

We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and…

Living materials such as membranes, cytoskeletal assemblies, cell collectives and tissues can often be described as active solids -- materials that are energized from within, with elastic response about a well defined reference…

We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs.

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…

The rotor-router model on a graph describes a discrete-time walk accompanied by the deterministic evolution of configurations of rotors randomly placed on vertices of the graph. We prove the following property: if at some moment of time,…

We find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our…

This article surveys results for Riemannian manifolds of positive and non-negative sectional curvature with symmetries.

There are two primary goals to this paper. In the first part of the paper we study smooth metric measure spaces (M^n,g,e^{-f}dv_g) and give several ways of characterizing bounds -Kg\leq \Ric+\nabla^2f\leq Kg on the Ricci curvature of the…

We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well known gap in the spectrum of the Laplacian on the upper half-plane with hyperbolic metric. We make some…

We study the $(2+2)$-Einstein warped product manifolds, where the scalar curvature of the Base is a multiple of the warping function, and we called this condition (inside a warped product manifold) $f$-curvature-Base ($R_{f_B}$).The aim of…

Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.

In this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci curvature on a given high-dimensional Spin-manifold have many…

We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition,…

In this paper, we show that the Ricci curvature lower bound in Ollivier's Wasserstein metric sense of a continuous time jumping Markov process on a graph can be characterized by some optimal coupling generator and provide the construction…

We study the mixing properties of a Brownian motion whose movements are hindered by semipermeable barriers. Our setting assumes that the process takes values in a smooth planar domain and that the barriers are one-dimensional closed curves.…

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase…

A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…

Earlier work of the first author examined two boundary value problems associated to the Gauss Curvature Flow on a surface of revolution generated by a positive, differentiable function on a compact interval. In this continuation, two…