• Publications
  • Influence
Riemannian geometry and geometric analysis
* Established textbook * Continues to lead its readers to some of the hottest topics of contemporary mathematical research This established reference work continues to lead its readers to some of
Two-dimensional geometric variational problems
Part 1 Examples, definitions, and elementary results: Plateau's problem two dimensional conformally invariant variational problems harmonic maps, conformal maps and holomorphic quadratic
Nonpositive Curvature: Geometric And Analytic Aspects
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
Ollivier’s Ricci Curvature, Local Clustering and Curvature-Dimension Inequalities on Graphs
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.
Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
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
Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplacian
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
Bernstein type theorems for higher codimension
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