19 citations · 122 across the 20 of their papers we have counts for
6 papers · 1 filter
Lipschitz-Volume rigidity and Sobolev coarea inequality for metric surfaces
Damaris Meier, Dimitrios Ntalampekos
We prove that every 1-Lipschitz map from a closed metric surface onto a closed Riemannian surface that has the same area is an isometry. If we replace the target space with a non-s…
Polyhedral approximation and uniformization for non-length surfaces
Dimitrios Ntalampekos, Matthew Romney
We prove that any metric surface (that is, metric space homeomorphic to a 2-manifold with boundary) with locally finite Hausdorff 2-measure is the Gromov-Hausdorff limit of polyhed…
Polyhedral approximation of metric surfaces and applications to uniformization
Dimitrios Ntalampekos, Matthew Romney
We prove that any length metric space homeomorphic to a 2-manifold with boundary, also called a length surface, is the Gromov-Hausdorff limit of polyhedral surfaces with controlled…
Non-removability of Sierpinski spaces
Dimitrios Ntalampekos, Jang-Mei Wu
We prove that all Sierpiński spaces in , , are non-removable for (quasi)conformal maps, generalizing the result of the first named author arXiv:1809.05605.…
Potential theory on Sierpinski carpets with applications to uniformization
Dimitrios Ntalampekos
This research is motivated by the study of the geometry of fractal sets and is focused on uniformization problems: transformation of sets to canonical sets, using maps that preserv…
Non-removability of the Sierpinski Gasket
Dimitrios Ntalampekos
We prove that the Sierpiński gasket is non-removable for quasiconformal maps, thus answering a question of Bishop. The proof involves a new technique of constructing an exceptional…