 | Kigami J. Resistance forms, quasisymmetric maps, and heat kernel estimates. - Providence: American Mathematical Society, 2012. - v, 132 p.: ill. - (Memoirs of the American Mathematical Society; vol.216, N 1015). - Bibliogr.: p.123-125. - Ind.: p.131. - ISSN 0065-9266; ISBN 978-0-8218-5299-6
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Chapter 1 Introduction ......................................... 1
Part 1 Resistance forms and heat kernels ....................... 7
Chapter 2 Topology associated with a subspace of functions ..... 9
Chapter 3 Basics on resistance forms .......................... 13
Chapter 4 The Green function .................................. 17
Chapter 5 Topologies associated with resistance forms ......... 21
Chapter 6 Regularity of resistance forms ...................... 25
Chapter 7 Annulus comparable condition and local property ..... 27
Chapter 8 Trace of resistance form ............................ 31
Chapter 9 Resistance forms as Dirichlet forms ................. 35
Chapter 10 Transition density .................................. 39
Part 2 Quasisymmetric metrics and volume doubling measures .... 47
Chapter 11 Semi-quasisymmetric metrics ......................... 49
Chapter 12 Quasisymmetric metrics .............................. 53
Chapter 13 Relations of measures and metrics ................... 55
Chapter 14 Construction of quasisymmetric metrics .............. 61
Part 3 Volume doubling measures and heat kernel estimates ..... 65
Chapter 15 Main results on heat kernel estimates ............... 67
Chapter 16 Example: the α-stable process on  .................. 73
Chapter 17 Basic tools in heat kernel estimates ................ 77
Chapter 18 Proof of Theorem 15.6 ............................... 83
Chapter 19 Proof of Theorems 15.10, 15.11 and 15.13 ............ 87
Part 4 Random Sierpinski gaskets .............................. 91
Chapter 20 Generalized Sierpinski gasket ....................... 93
Chapter 21 Random Sierpinski gasket ............................ 99
Chapter 22 Resistance forms on Random Sierpinski gaskets ...... 103
Chapter 23 Volume doubling property ........................... 109
Chapter 24 Homogeneous case ................................... 115
Chapter 25 Introducing randomness ............................. 121
Bibliography .................................................. 123
Assumptions, Conditions and Properties in Parentheses ......... 127
List of Notations ............................................. 129
Index ......................................................... 131
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