Heat Kernel Bounds for the Laplacian on Metric Graphs of Polygonal Tilings

Abstract

We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.

8 pages

References in corpus (2)

• Stability of parabolic Harnack inequalities on metric measure spaces
• Gaussian estimates for a heat equation on a network

Cited by in corpus (1)

• Schrödinger and polyharmonic operators on infinite graphs: Parabolic well-posedness and p-independence of spectra