OSCILLATION AND DIMENSIONS OF HARMONIC FUNCTIONS ON THE SIERPIŃSKI GASKETS

Zhen Liang and Huo-Jun Ruan ()
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Zhen Liang: School of Mathematics, Nanjing Audit University, Nanjing 211815, P. R. China
Huo-Jun Ruan: School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-6

Abstract: In this paper, we estimate the oscillation of harmonic functions on the (N − 1)-dimensional Sierpiński gasket KN, where K3 is the classical Sierpiński gasket. By using this result, we prove that both the box dimension and the Hausdorff dimension of graphs of harmonic functions on KN are log2N.

Keywords: Sierpiński Gasket; Hausdorff Dimension; Box Dimension; Harmonic Function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501342

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