Metrics of Hyperbolic Type on Bounded Fractals |
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Authors: | V Metz |
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Institution: | (1) Faculty of Mathematics, Bielefeld University, 33501 Bielefeld, Germany |
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Abstract: | On the bounded Sierpinski gasket F we use the set of essential fixed points V
0 as a boundary and consider the fractal Brownian motion on F killed in V
0. The corresponding Dirichlet–Laplacian is described in terms of a kind of hyperbolic distance, a metric which explodes near
the boundary. We consider Harnack inequalities, Green’s function estimates and (random) products of matrices defining the
local energy of harmonic functions.
Supported by the DFG research group ‘Spektrale Analysis, asymptotische Verteilungen und stochastische Dynamik.’ |
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Keywords: | killed Brownian motion Green’ s function hyperbolic metric fractals |
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