Related papers: Cheeger type inequalities associated with isocapac…

The problem of multiway partitioning of an undirected graph is considered. A spectral method is used, where the k > 2 largest eigenvalues of the normalized adjacency matrix (equivalently, the k smallest eigenvalues of the normalized graph…

This work investigates upper bounds for the spectrum of the Steklov-type operator on Riemannian manifolds with boundary. We extend the Fraser-Schoen estimate for the first positive Steklov eigenvalue to higher Steklov eigenvalues, in terms…

We consider non-negative $\sigma$-finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant…

We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue…

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of "symmetric exponential" processes compared to the Gaussian ones in…

We present a Diaz--Metcalf type operator inequality as a reverse Cauchy-Schwarz inequality and then apply it to get the operator versions of P\'{o}lya-Szeg\"{o}'s, Greub-Rheinboldt's, Kantorovich's, Shisha-Mond's, Schweitzer's, Cassels' and…

In this paper, we present a Lichnerowicz type estimate and (higher order) Buser type estimates for the magnetic Laplacian on a closed Riemannian manifold with a magnetic potential. These results relate eigenvalues, magnetic fields, Ricci…

We introduce a curvature function for planar graphs to study the connection between the curvature and the geometric and spectral properties of the graph. We show that non-positive curvature implies that the graph is infinite and locally…

In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus…

We investigate some analytic properties of traces of Dirichlet forms with respect to measures satisfying Hardy-type inequality. Among other results we prove convergence of spectra, ordered eigenvalues, eigenfunctions as well as convergence…

We provide a quantitative lower bound to the Cheeger constant of a set $\Omega$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide examples which show that these quantitative estimates are…

We relate the nontrivial singular values $\sigma_2,\ldots,\sigma_n$ of the normalized adjacency matrix of an Eulerian directed graph to combinatorial measures of graph expansion: \\ 1. We introduce a new directed analogue of conductance…

The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a ``transmission`` system. A transmission system is a mathematical representation of a means of transmitting…

We introduce the notion of quasimonotone polar of a multivalued operator, in a similar way as the well-known monotone polar due to Martinez-Legaz and Svaiter. We first recover several properties similar to the monotone polar, including a…

There is a recently discovered connection between the spectral theory of Schr\"o-dinger operators whose potentials exhibit aperiodic order and that of Laplacians associated with actions of groups on regular rooted trees, as Grigorchuk's…

The Steklov eigenvalue problem was introduced over a century ago, and its discrete form attracted interest recently. Let $D$ and $\delta \Omega$ be the maximum vertex degree and the set of vertices of degree one in a graph $\mathcal{G}$…

In this paper we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal…

We introduce three biharmonic Steklov problems on differential forms with Neumann boundary conditions and show that they are elliptic. We prove the existence of a discrete spectrum for each of those problems and give associated variational…

We establish mild conditions under which a possibly irregular, sparse graph $G$ has "many" strong orientations. Given a graph $G$ on $n$ vertices, orient each edge in either direction with probability $1/2$ independently. We show that if…

We use two variational techniques to prove upper bounds for sums of the lowest several eigenvalues of matrices associated with finite, simple, combinatorial graphs. These include estimates for the adjacency matrix of a graph and for both…