6 papers
Nonexistence Results for Semilinear Parabolic and Hyperbolic Equations on Metric Graphs
Yang Liu, Yong Lin, Haohang Zhang
This paper investigates the nonexistence of solutions to semilinear parabolic and hyperbolic inequalities with positive potentials on metric graphs, including both nonnegative solu…
Nonexistence results for semilinear elliptic equations on metric graphs
Yang Liu, Yong Lin, Haohang Zhang
In this paper, we study the nonexistence of solutions to semilinear elliptic equations with a positive potential on metric graphs. In particular, the Laplacian under consideration…
Inequalities between Dirichlet and Neumann Eigenvalues on Surfaces
Bobo Hua, Florentin Münch, Haohang Zhang
For a bounded Lipschitz domain in a Riemannian surface satisfying certain curvature condition, we prove that where ( resp.) is the -…
Eigenvalues of the Hodge Laplacian on digraphs
Alexander Grigor'yan, Yong Lin, S. -T. Yau +1
This paper aims to compute and estimate the eigenvalues of the Hodge Laplacians on directed graphs. We have devised a new method for computing Hodge spectra with the following two…
Connection Laplacian on discrete tori with converging property
Yong Lin, Shi Wan, Haohang Zhang
This paper presents a comprehensive analysis of the spectral properties of the connection Laplacian for both real and discrete tori. We introduce novel methods to examine these eig…
Graphs on surfaces with positive Forman curvature or corner curvature
Yohji Akama, Bobo Hua, Yanhui Su +1
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof fo…