Assistant Professor
Mathematics Department
Stony Brook University
Stony Brook, NY, 11794-3651
Office: Math Tower 3-117
Contact: dimitrios.ntalampekos

stonybrook

edu
Research:
My primary research interests lie in the field of analysis on metric spaces. More specifically, my research focuses on uniformization and rigidity problems in metric spaces, as well as, on the study of the quasiconformal geometry of fractal sets. I am also interested in applications to complex dynamics and to fractals arising in probability.
My research is partially supported by NSF Grant DMS-2000096.
The
Analysis Seminar at Stony Brook University.
Preprints
-
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
-
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. (2022), to appear.
[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]
Thesis
Events
CAFT 2018 - New Developments in Complex Analysis and Function Theory, Heraklion, Greece, July 2-6, 2018