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A tale of two fractals A. A. Kirillov - Penn Math

A tale of two fractalsA. A. KirillovDepartment of Mathematics, The University of Pennsylva-nia, Philadelphia, PA 19104-6395E-mail address: Ben and LisaThe author deeply thanks the Erwin Schro odinger International Institutefor Mathematical Physics (ESI) where this work was started, the MaxPlanck Institute in Bonn (MPI), and the Institute des Hautes EtudesScientifique (IHES) where it was also thank the referees for helpful 1. Sierpi nski gasket7 Chapter 1. Definition and general First appearance and naive definition9 Info A. Metric Definition of self-similar fractals15 Info B. Hausdorff measure and Hausdorff dimension20 Chapter 2. Laplace operator on Sierpi nski gasket23 Info C. Laplace operator and harmonic Laplace operator Comparing spectra of nand of n Eigenfunctions of Laplace operator onSN31 Chapter 3.

A tale of two fractals A. A. Kirillov Department of Mathematics, The University of Pennsylva-nia, Philadelphia, PA 19104-6395 E-mail address: kirillov@math.upenn.edu

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