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This established reference work continues to lead its readers to some of… Expand

Part 1 Examples, definitions, and elementary results: Plateau's problem two dimensional conformally invariant variational problems harmonic maps, conformal maps and holomorphic quadratic… Expand

1 Introduction.- 1.1 Examples of Riemannian manifolds of negative or nonpositive sectional curvature.- Appendix to 1.1: Symmetric spaces of noncompact type.- 1.2 Mordell and Shafarevitch type… Expand

This paper employs a definition of generalized Ricci curvature proposed by Ollivier in a general framework of Markov processes and metric spaces and applied in graph theory by Lin–Yau to derive lower RicCI curvature bounds on graphs in terms of such local clustering coefficients.Expand

We prove the following estimate for the spectrum of the normalized Laplace operator $\Delta$ on a finite graph $G$, \begin{equation*}1- (1- k[t])^{\frac{1}{t}}\leq \lambda_1 \leq \cdots \leq… Expand

We study the spectrum of the normalized Laplace operator of a connected graph $\Gamma$. As is well known, the smallest nontrivial eigenvalue measures how difficult it is to decompose $\Gamma$ into… Expand

Abstract. We show a Bernstein theorem for minimal graphs of arbitrary dimension and codimension under a bound on the slope that improves previous results and is independent of the dimension and… Expand