Dimitrios Ntalampekos

Research

My primary research interests lie in the fields of Complex Analysis and Analysis on Metric Spaces. Topics include uniformization and rigidity problems in the plane and in metric spaces, quasiconformal geometry of fractal surfaces and metric spaces, and complex dynamics. My current work often relies on an extension of classical results in geometry and analysis to a non-smooth or fractal setting.

Research grants: NSF Grant DMS-2000096, NSF Grant DMS-2246485.

Other grants: Quasiworld Workshop NSF Grant DMS-2246679.

    Preprints

  1. Metric surfaces and conformally removable sets in the plane
    Submitted. [arXiv]
  2. Piecewise quasiconformal dynamical systems of the unit circle (joint with Yusheng Luo)
    [preprint]
  3. Uniformization of Gromov hyperbolic domains by circle domains (joint with Christina Karafyllia)
    Submitted. [arXiv]
  4. Exhaustions of circle domains (joint with Kai Rajala)
    Submitted. [arXiv]

    5. Monographs

  5. Potential Theory on Sierpiński Carpets With Applications To Uniformization
    Lecture Notes in Mathematics, vol. 2268, Springer, Cham, 2020. [published version] [arXiv] [poster]

    6. Publications

  6. Polyhedral approximation and uniformization for non-length surfaces (joint with Matthew Romney)
    J. Eur. Math. Soc., to appear. [journal] [arXiv] [slides]
  7. CNED sets: countably negligible for extremal distances
    Selecta Math. (N.S.) 30 (2024), no. 4, Paper No. 61, 57pp. [journal] [journal (free access)] [arXiv] [arXiv long version] [slides]
  8. Lipschitz-volume rigidity and Sobolev coarea inequality for metric surfaces (joint with Damaris Meier)
    J. Geom. Anal. 34 (2024), no. 5, Paper No. 128, 30pp. [journal] [journal (free access)] [arXiv] [slides]
  9. David extension of circle homeomorphisms, welding, mating, and removability (joint with Misha Lyubich, Sergei Merenkov, and Sabyasachi Mukherjee)
    Mem. Amer. Math. Soc., to appear. [arXiv]
  10. Metric definition of quasiconformality and exceptional sets
    Math. Ann. 389 (2024), no. 3, 3231-3253. [journal] [journal (free access)] [arXiv] [slides]
  11. Conformal uniformization of planar packings by disk packings
    Adv. Math. 428 (2023), Paper No. 109159, 58pp. [journal] [arXiv]
  12. Rigidity and continuous extension for conformal maps of circle domains
    Trans. Amer. Math. Soc. 376 (2023), no. 7, 5221-5239. [journal] [arXiv]
  13. Polyhedral approximation of metric surfaces and applications to uniformization (joint with Matthew Romney)
    Duke Math. J. 172 (2023), no. 9, 1673-1734. [journal] [arXiv] [slides]
  14. Extension of boundary homeomorphisms to mappings of finite distortion (joint with Christina Karafyllia)
    Proc. Lond. Math. Soc. 125 (2022), no. 3, 488-510. [journal] [journal (free access)] [arXiv] [slides]
  15. On the Hausdorff dimension of the residual set of a packing by smooth curves (joint with Steven Maio)
    J. Lond. Math. Soc. 105 (2022), no. 3, 1752-1786. [journal] [journal (free access)] [arXiv]
  16. Monotone Sobolev Functions in Planar Domains: Level Sets and Smooth Approximation
    Arch. Ration. Mech. Anal. 238 (2020), no. 3, 1199-1230. [journal] [journal (free access)] [arXiv]
  17. Falconer's \((K,d)\) distance set conjecture can fail for strictly convex sets \(K\) in \(\mathbb R^d\) (joint with Christopher Bishop and Hindy Drillick)
    Rev. Mat. Iberoam. 37 (2021), no. 5, 1953-1968. [journal] [preprint]
  18. Rigidity theorems for circle domains (joint with Malik Younsi)
    Invent. Math. 220 (2020), no. 1, 129-183. [journal] [journal (free access)] [arXiv] [slides]
  19. On the inverse absolute continuity of quasiconformal mappings on hypersurfaces (joint with Matthew Romney)
    Amer. J. Math. 143 (2021), no. 5, 1633-1659. [journal] [arXiv] [slides]
  20. Non-removability of Sierpiński spaces (joint with Jang-Mei Wu)
    Proc. Amer. Math. Soc. 148 (2020), 203-212. [journal] [arXiv]
  21. Non-removability of Sierpiński carpets
    Indiana Univ. Math. J. 70 (2021), no. 3, 847-854. [journal] [arXiv]
  22. Non-removability of the Sierpiński gasket
    Invent. Math. 216 (2019), no. 2, 519-595. [journal] [journal (free access)] [arXiv] [slides]
  23. A removability theorem for Sobolev functions and detour sets
    Math. Z. 296 (2020), 41-72. [journal] [journal (free access)] [arXiv]
  24. Semi-hyperbolic rational maps and size of Fatou components
    Ann. Acad. Sci. Fenn. Math. 43 (2018), 425-446. [journal] [arXiv]

Thesis

Potential theory on Sierpiński carpets with applications to uniformization
Ph.D. dissertation, UCLA (2018). [ProQuest] [eScholarship]