Preprints and Lecture Note

12. "Geometry of metric spaces via weighted partitions by trees"
9/23/2016 version 1(pdf)
9/19/2017 version 2(pdf)(Grammartical errors and tyops are fixed.)

11. "Completely symmetric resistance forms on the stretched Sierpinski gasket"
       with P. Alonso Ruiz and U. Freiberg
6/29/2016 version 1(pdf)
To appear in Journal of Fractal Geometry

10. "Time changes of the Brownian motion: Poincare inequality, heat kernel estimate and protodistance"
4/9/2015 version 1.0(pdf)
10/19/2016 final version(pdf)
To appear in Memoirs of American Mathematical Society

9. "Transitions on a noncompact Cantor set and random walks on its defining tree"
5/31/2012 final version pdf(311KB)
(Ann. Inst. Henri Poincaré Probab. Stat. 49 (2013), no. 4, 1090–1129)

8. "Quasisymmetric modification of metrics on self-similar sets"@@
9/16/2010 version 1.0 pdf(320KB)
(in "Geometry and analysis of fractals", 253–282, Springer Proc. Math. Stat., 88, Springer, Heidelberg, 2014)

7. Lecture Note: "Resistance forms, quasisymmetric maps and heat kernel estimates"
June 1 - June 4, Workshop: Analysis and Geometry on Fractals at Fourier Institute, Grenoble, France
pdf(128KB)

6. "Dirichlet forms and associated heat kernels on the Cantor set
induced by random walks on trees"
Advances in Mathemtaics 225(2010) 2674-2730
10/5/2009   version 1.0 pdf(372KB)
10/27/2009 version 1.2 pdf(372KB)
5/21/2010 version 2.1 pdf(344KB) Final version

Version 1.2 is more self-contained. However, version 2.1 contains several new results
on capacities of points and martingales associated with harmonic functions. Moreover,
the proof of the main theorem is simpler.

5. "Resistance forms, quasisymmetric maps and heat kernel estimates"
Memoirs of the American Mathematical Society, vol 216(2012), no. 1015
7/8/2008 version 1.0
6/24/2009 version 2.0 pdf(598KB)
8/20/2010 version 3.0 pdf(692KB): Final version: Indexes and new sections are added

4. "Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka
measure and the Gaussian heat kernel estimate"
(Math. Ann., vol 340 (2008) 781-804, Springer Link)
2/1/2007 version 1.0
8/28/2007 version 2.1 pdf(424KB)

3. "Volume doubling measures and heat kernel estimates on self-similar sets"
(Memoirs of the American Mathematical Society, vol. 199, Number 932, 2009)
 5/26/2005 version1.0
12/30/2007 version4.0(Final)
                   pdf(1.8MB)
                   dvi(480KB)


2. "Local Nash inequality and inhomogeneity of heat kernels"
(Proceedings of the London Mathematical Society (3), vol.89 (2004) 525-544)
4/22/2003 version 1.1
1/28/2004 version 2   pdf

1. "Harmonic analysis for resistance forms"
(Journal of Functional Analysis, vol. 204(2003) 399-444) pdf


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