Conformal energy, conformal Laplacian, and energy measures on the Sierpinski gasket
نویسندگان
چکیده
منابع مشابه
Conformal Energy, Conformal Laplacian, and Energy Measures on the Sierpinski Gasket
On the Sierpinski Gasket (SG) and related fractals, we define a notion of conformal energy Eφ and conformal Laplacian ∆φ for a given conformal factor φ, based on the corresponding notions in Riemannian geometry in dimension n 6= 2. We derive a differential equation that describes the dependence of the effective resistances of Eφ on φ. We show that the spectrum of∆φ (Dirichlet or Neumann) has si...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2007
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-04363-2