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  1. No Access

    Article

    Payne–Polya–Weinberger, Hile–Protter and Yang’s Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices

    In this paper, we prove some analogues of Payne–Polya–Weinberger, Hile–Protter and Yang’s inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice

    Bobo Hua, Yong Lin, Yanhui Su in The Journal of Geometric Analysis (2023)

  2. Article

    Open Access

    Discrete Tori and Trigonometric Sums

    We prove a discrete analogue of the Poisson summation formula.

    Alexander Grigor’yan, Yong Lin, Shing-Tung Yau in The Journal of Geometric Analysis (2022)

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  3. No Access

    Article

    Calculus of variations on locally finite graphs

    Let \(G=(V,E)\) G = ( V ...

    Yong Lin, Yunyan Yang in Revista Matemática Complutense (2022)

  4. No Access

    Article

    A heat flow for the mean field equation on a finite graph

    Inspired by works of Castéras (Pac J Math 276:321–345, 2015), Li and Zhu (Calc Var Partial Differ Equ 58:1–18, 2019), Sun and Zhu (Calc Var Partial Differ Equ 60:1–26, 2021), we propose a heat flow for the mea...

    Yong Lin, Yunyan Yang in Calculus of Variations and Partial Differential Equations (2021)

  5. No Access

    Article

    Heat kernels on forms defined on a subgraph of a complete graph

    We study the heat kernel expansion of the Laplacian on n-forms defined on a subgraph of a directed complete graph. We derive two expressions for the subgraph heat kernel on 0-forms and compute the coefficients of...

    Yong Lin, Sze-Man Ngai, Shing-Tung Yau in Mathematische Annalen (2021)

  6. No Access

    Article

    Path Complexes and their Homologies

    We introduce the notions of a path complex and its homologies. Particular cases of path homologies are simplicial homologies and digraph homologies. We state and prove some properties of path homologies, in pa...

    A. A. Grigor’yan, Yong Lin, Yu. V. Muranov… in Journal of Mathematical Sciences (2020)

  7. No Access

    Article

    Ultracontractivity and Functional Inequalities on Infinite Graphs

    We prove the equivalence between some functional inequalities and the ultracontractivity property of the heat semigroup on infinite graphs. These functional inequalities include Sobolev inequalities, Nash ineq...

    Yong Lin, Shuang Liu, Hongye Song in Discrete & Computational Geometry (2019)

  8. No Access

    Article

    Equivalent properties for CD inequalities on graphs with unbounded Laplacians

    The CD inequalities are introduced to imply the gradient estimate of Laplace operator on graphs. This article is based on the unbounded Laplacians, and finally concludes some equivalent properties of the CD(K,...

    Chao Gong, Yong Lin in Chinese Annals of Mathematics, Series B (2017)

  9. No Access

    Article

    The existence and nonexistence of global solutions for a semilinear heat equation on graphs

    Let \(G=(V,E)\) G = ...

    Yong Lin, Yiting Wu in Calculus of Variations and Partial Differential Equations (2017)

  10. No Access

    Article

    Existence of positive solutions to some nonlinear equations on locally finite graphs

    Let G = (V, E) be a locally finite graph, whose measure μ(x) has positive lower bound, and Δ be the usual graph Laplacian. Applying the mountain-pass theorem due to Ambrosetti and Rabinowitz (1973), we establish ...

    Alexander Grigor’yan, Yong Lin, YunYan Yang in Science China Mathematics (2017)

  11. No Access

    Article

    A Gradient Estimate for Positive Functions on Graphs

    We derive a gradient estimate for positive functions, in particular for positive solutions to the heat equation, on finite or locally finite graphs. Unlike the well known Li-Yau estimate, which is based on the...

    Yong Lin, Shuang Liu, Yunyan Yang in The Journal of Geometric Analysis (2017)

  12. No Access

    Article

    Global gradient estimate on graph and its applications

    Continuing our previous work (ar**v:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs...

    Yong Lin, Shuang Liu, Yun Yan Yang in Acta Mathematica Sinica, English Series (2016)

  13. No Access

    Article

    Curvature notions on graphs

    We survey some geometric and analytic results under the assumptions of combinatorial curvature bounds for planar/semiplanar graphs and curvature dimension conditions for general graphs.

    Bobo Hua, Yong Lin in Frontiers of Mathematics in China (2016)

  14. No Access

    Article

    Kazdan–Warner equation on graph

    Let \(G=(V,E)\) G = ...

    Alexander Grigor’yan, Yong Lin, Yunyan Yang in Calculus of Variations and Partial Differe… (2016)