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Resistance forms, quasisymmetric maps, and heat kernel estimates / Jun Kigami.

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Author/Creator:
Kigami, Jun.
Language:
English.
Publication date:
2011
Imprint:
Providence, R.I. : American Mathematical Society, 2012, c2011.
Format:
  • Book
  • v, 132 p. : ill. ; 26 cm.
Note:
"Volume 216, number 1015 (first of 4 numbers)."
Bibliography:
Includes bibliographical references (p. 123-25) and index.
Contents:
  • Introduction
  • Topology associated with a subspace of functions
  • Basics on resistance forms
  • The Green function
  • Topologies associated with resistance forms
  • Regularity of resistance forms
  • Annulus comparable condition and local property
  • Trace of resistance form
  • Resistance forms as Dirichlet forms
  • Transition density
  • Semi-quasisymmetric metrics
  • Quasisymmetric metrics
  • Relations of measures and metrics
  • Construction of quasisymmetric metrics
  • Main results on heat kernel estimates
  • Example: the a-stable process on R
  • Basic tools in heat kernel estimates
  • Proof of theorem 15.6
  • Proof of theorems 15.10, 15.11 and 15.13
  • Generalized Sierpinski gasket
  • Random Sierpinski gasket
  • Resistance forms on random Sierpinski gaskets
  • Volume doubling property
  • Homogenous case
  • Introducing randomness.
Series:
Memoirs of the American Mathematical Society, 0065-9266 ; no. 1015
Memoirs of the American Mathematical Society ; no. 1015.
Subjects:
ISBN:
9780821852996
082185299X

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