# Dimitrios Ntalampekos

Assistant Professor
Mathematics Department
Stony Brook University
Stony Brook, NY, 11794-3651

Office: Math Tower 3-117

Contact: dimitrios.ntalampekosstonybrookedu

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.

My research is partially supported by NSF Grant DMS-2000096.

## Preprints

• Conformal uniformization of planar packings by disk packings
Submitted. [arXiv]
• Polyhedral approximation and uniformization for non-length surfaces (joint with Matthew Romney)
Submitted. [arXiv]
• Definitions of quasiconformality and exceptional sets
Submitted. [arXiv]
• David extension of circle homeomorphisms, welding, mating, and removability (joint with Misha Lyubich, Sergei Merenkov, and Sabyasachi Mukherjee)
Submitted. [arXiv]

## Monographs

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

## Publications

• Rigidity and continuous extension for conformal maps of circle domains
Trans. Amer. Math. Soc. (2023), to appear. [arXiv]
• Polyhedral approximation of metric surfaces and applications to uniformization (joint with Matthew Romney)
Duke Math. J. (2022), to appear. [arXiv]
• 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]
• 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]
• 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]
• 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]
• Rigidity theorems for circle domains (joint with Malik Younsi)
Invent. Math. 220 (2020), no. 1, 129-183. [journal] [journal (free access)] [arXiv] [slides]
• 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]
• Non-removability of Sierpiński spaces (joint with Jang-Mei Wu)
Proc. Amer. Math. Soc. 148 (2020), 203-212. [journal] [arXiv]
• Non-removability of Sierpiński carpets
Indiana Univ. Math. J. 70 (2021), no. 3, 847-854. [journal] [arXiv]
• Non-removability of the Sierpiński gasket
Invent. Math. 216 (2019), no. 2, 519-595. [journal] [journal (free access)] [arXiv] [slides]
• A removability theorem for Sobolev functions and detour sets
Math. Z. 296 (2020), 41-72. [journal] [journal (free access)] [arXiv]
• Semi-hyperbolic rational maps and size of Fatou components
Ann. Acad. Sci. Fenn. Math. 43 (2018), 425-446. [journal] [arXiv]