Removable sets for Lipschitz harmonic functions in the plane

By G. David, P. Mattila. 2000

130 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dcc1acee43920cae3eb92f2fd86b1db29b2456ea

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Removable sets for continuous solutions of quasilinear elliptic equations (2001, background): “David and Mattila [ DM ] treated the case n = p = 2: a compact set E of nite 1-Hausdor measure is removable for Lipschitz continuous harmonic functions if and only if E is purely unrectiable.”
A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition (2000, result): “This result has already appeared in previous works ([ DM ], [NTV2]) and it plays a basic role in [To2] and [To4 ]t oo.”
The fall of the doubling condition in Calderón-Zygmund theory (2002, methodology): “It is a beautiful simple idea, which appeared for the first time in [ DM ] and was used to prove (12) in [T3].”
TheTb-theorem on non-homogeneous spaces (2003, methodology): “An application of the Tl- theorem: electric intensity capacity As a possible application of our non-homogeneous Tl - theorem we will cite the following result about the so-called electric intensity capacity (also known as harmonic Lipschitz capacity, see [11], [14], [16], [31] for some interesting r”
The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions (2012, unknown): “Then, E is removable for Lipschitz harmonic functions in Rn+1 if and only if E is purely n-unrectiﬁable. Again, this theorem was already known in the case n = 1. It was proved by David and Mattila in [DM]. The analogous result for the removable singularities for bounded analytic functions is the cel”
The Tb-theorem on non-homogeneous spaces that proves a conjecture of Vitushkin (2014, methodology): “977 for small Lipschitz constants: this turned out to be suﬃcient for the “only if” part). The “if” part was considered to be super diﬃcult. Finally it was proved by Guy David in 1997 [D1] using also [DM]. But actually this was only the “analytic part” of the proof. The “geometric part” was fortunat”