Harmonic functions of polynomial growth on infinite penny graphs
Zunwu He, Bobo Hua
TL;DR
This paper investigates the space of harmonic functions with polynomial growth on infinite penny graphs, establishing sharp estimates for their finite-dimensionality.
Contribution
It provides the first asymptotically sharp dimensional estimates for harmonic functions of polynomial growth on infinite penny graphs.
Findings
Finite-dimensionality of harmonic functions on penny graphs
Asymptotically sharp dimensional estimates
Extension to ancient solutions of the heat equation
Abstract
For an infinite penny graph, we study the finite-dimensional property for the space of harmonic functions, or ancient solutions of the heat equation, of polynomial growth. We prove the asymptotically sharp dimensional estimate for the above spaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering · Mathematical Dynamics and Fractals