Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs

By Fan Chung, Alexander Grigorʼyan, Shing-Tung Yau. 2000

90 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8465abc8b655b86f5009305ed32882bfece72475

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Kazdan-Warner equation on infinite graphs (2017, background): “elated to each other. They all reveal some geometric information of a manifold (or a graph). By now, there is a vital interest in the study of these objects on ﬁnite or inﬁnite graphs. See[1][2][4][5][8][9][16][20] for more related works. Generally, the Kazdan-Warner equation may not have a global s”
Ricci curvature of graphs (2011, background): “Many pioneering works were done by Chung, Yau, and their coauthors [3, 4, 5, 8, 9, 10, 12, 13, 14, 16, 15].”
Upper Bounds of Heat Kernels on Doubling Spaces (2014, background): “The arguments are known in the setting of manifolds, see for example [19], [15], [16], [9].”
Eigenvalues of elliptic operators and geometric applications (2004, background): “(see for example [10], [41], [22]), where c > 0 is an absolute constant.”
Modified Logarithmic Sobolev Inequalities in Discrete Settings (2006, unknown): “Yau [11], where the bounds are of the type D c √ d λ1 log |G|, for some universal constant c > 0.”
Li–Yau inequality on finite graphs via non-linear curvature dimension conditions (2014, methodology): “al condition P0f= ffor all f∈ C(V). (4) If the initial condition f∈ C(V) is positive, then Ptf∈ C(V) is also positive for all t≥ 0. This proposition is a standard one and a proof can be found e.g. in [9]. Theorem 4.5 (Semigroup form of the ψ-Li-Yau inequality). Let ψ ∈ C1(R+), and let G= (V,E) be a ”
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation (2011, background): “[5] and carry over easily to our setting.”