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math.CA2020★ 4 cited
On the Hausdorff dimension of the residual set of a packing by smooth curves
Steven Maio, Dimitrios Ntalampekos
Let a planar residual set be a set obtained by removing countably many disjoint topological disks from an open set in the plane. We prove that the residual set of a planar packing…
math.CA2019★ 5 cited
Monotone Sobolev functions in planar domains: level sets and smooth approximation
Dimitrios Ntalampekos
We prove that almost every level set of a Sobolev function in a planar domain consists of points, Jordan curves, or homeomorphic copies of an interval. For monotone Sobolev functio…
math.CA2017★ 4 cited
A removability theorem for Sobolev functions and detour sets
Dimitrios Ntalampekos
We study the removability of compact sets for continuous Sobolev functions. In particular, we focus on sets with infinitely many complementary components, called "detour sets", whi…