Papers

Preprints
  1. Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces [arXiv], submitted
    Joint with Riku Anttila and Sylvester Eriksson-Bique
  2. Characterizations of Sobolev functions via Besov-type energy functionals in fractals [arXiv], submitted
  3. Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces [arXiv], submitted
    Joint with Takashi Kumagai and Nageswari Shanmugalingam
  4. Contraction properties and differentiability of \( p \)-energy forms with applications to nonlinear potential theory on self-similar sets [arXiv], submitted
    Joint with Naotaka Kajino
  5. \( p \)-Energy forms on fractals: recent progress, [arXiv], submitted
    Joint with Naotaka Kajino
Published or Accepted papers
  1. First-order Sobolev spaces, self-similar energies and energy measures on the Sierpiński carpet [pdf] (Shorter version) [arXiv] (Long version),
    Joint with Mathav Murugan
    Comm. Pure Appl. Math. (2025, Early View).
  2. Korevaar–-Schoen \( p \)-energy forms and associated energy measures on fractals [arXiv]
    Joint with Naotaka Kajino
    Springer Tohoku Series in Mathematics, accepted.
  3. Construction of \( p \)-energy and associated energy measures on Sierpiński carpets [arXiv]
    Trans. Amer. Math. Soc. 377 (2024), no. 2, 951–1032.
  4. Parabolic index of an infinite graph and Ahlfors regular conformal dimension of a self-similar set; in "Analysis and partial differential equations on manifolds, fractals and graphs"
    de Gruyter series Advances in Analysis and Geometry 3 (2021), pp. 201-274.
Other publications (not refereed)
  1. Construction of Korevaar–Schoen \( p \)-energy forms and \( p \)-energy measures (joint work with Naotaka Kajino)
    Oberwolfach Report 42 (2024), 41-44.

Presentations

  1. Self-similar \( p \)-energy form and \( p \)-energy measures on the Sierpinski carpet, The 3rd Hong Kong/Kyoto Workshop on Fractal Geometry and Related Areas, The Chinese University of Hong Kong, Shatin, N.T, Hong Kong, March 2025
  2. On singularity of \( p \)-energy measures among distinct values of \( p \) for some p.-c.f. self-similar sets, Analysis Seminar, University of Jyväskylä, Jyväskylä, Finland, October 2024
  3. Construction of self-similar energy forms and self-similar energy measures on the Sierpinski carpet (contributed talk, 25 minutes), Fractal Geometry and Stochastics 7, Technical University of Chemnitz, Chemnitz (Saxony), Germany, September 2024
  4. Construction of Korevaar–Schoen \( p \)-energy forms and associated \( p \)-energy measures (short presentation, 10 minutes), Recent Developments in Dirichlet Form Theory and Related Fields, Mathematisches Forschungsinstitut Oberwolfach, Germany, September 2024
  5. [Poster] Self-similar \( p \)-energy form on the Sierpiński carpet, 2024 Open German-Japanese Conference on Stochastic Analysis and Applications, Hokkaido University, Sapporo, Japan, September 2024
  6. First-order Sobolev spaces and self-similar energies on the Sierpinski carpet, Geometric Analysis Seminar, University of Jyväskylä, Jyväskylä, Finland, March 2024
  7. [Poster] First-order Sobolev spaces on the Sierpiński carpet, French Japanese Conference on Probability & Interactions, IHES, Paris, France, March 2024
  8. Construction of first-order Sobolev spaces on the planar Sierpiński carpet, Random Interacting Systems, Scaling Limits, and Universality (Week 1) (short talk, 20 minutes), National University of Singapore, Singapore, December 2023
  9. [Poster] First-order Sobolev spaces on the Sierpiński carpet, Stochastic Processes and Related Fields, Kyoto University, Kyoto, Japan, September 2023
  10. Construction of a canonical \( p \)-energy on the Sierpiński carpet for all \( p > 1 \), Geometric and Stochastic analysis on metric space, Kyoto University, Kyoto, Japan, March 2023
  11. Nonlinear potential theory on the Sierpiński carpet, Analysis and geometry of fractals and metric spaces: Recent developments and future prospects (25 minutes), Bankoku Shinryokan, Okinawa, Japan, March 2023
  12. Construction of a canonical \( p \)-energy on the Sierpiński carpet, Smooth Functions on Rough Spaces and Fractals with Connections to Curvature Functional Inequalities (short talk, 20 minutes), BIRS, Banff, Canada, November 2022
  13. Construction of a canonical \( p \)-energy on the Sierpiński carpet, PIMS-CRM Summer School in Probability 2022 (short talk, 30 minutes), University of British Columbia, Vancouver, Canada, June 2022
  14. Construction of a canonical \( p \)-energy on the Sierpiński carpet, OIST Analysis on Metric Spaces Workshop 2022 (short talk via Zoom, 15 minutes), OIST, Okinawa (hybrid), Japan, May 2022
  15. Construction of a canonical \( p \)-energy on the Sierpiński carpet, Quasiworld, Zoom Webinar, October 2021
  16. Generalized resistance metrics on graphs, Kobe Workshop on Probabilistic Potential Theory and Related Fields, Kobe University, Kobe, Japan, May 2019