Mihalis Mourgoglou

activity

20102026

most citedRectifiability of harmonic measure

61 citations · 237 across the 33 of their papers we have counts for

collaborators

Showing 2016Show all

8 papers · 1 filter

math.CA2016★ 29 cited

Uniform rectifiability from Carleson measure estimates and $ε$ -approximability of bounded harmonic functions

John Garnett, Mihalis Mourgoglou, Xavier Tolsa

Let $Ω \subset R^{n + 1}$ , $n \geq 1$ , be a corkscrew domain with Ahlfors-David regular boundary. In this paper we prove that $\partial Ω$ is uniformly $n$ -rectifiable if every bo…

math.CA2016★ 18 cited

Uniform rectifiability, elliptic measure, square functions, and $ε$ -approximability via an ACF monotonicity formula

Jonas Azzam, John Garnett, Mihalis Mourgoglou +1

Let $Ω \subset R^{n + 1}$ , $n \geq 2$ , be an open set with Ahlfors-David regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ i…

math.CA2016

On a two-phase problem for harmonic measure in general domains

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa +1

We show that, for disjoint domains in the Euclidean space, mutual absolute continuity of their harmonic measures implies absolute continuity with respect to surface measure and rec…

math.CA2016★ 2 cited

Non-homogeneous square functions on general sets: suppression and big pieces methods

Henri Martikainen, Mihalis Mourgoglou, Emil Vuorinen

We aim to showcase the wide applicability and power of the big pieces and suppression methods in the theory of local $T b$ theorems. The setting is new: we consider conical square f…

math.CA2016★ 3 cited

The one-phase problem for harmonic measure in two-sided NTA domains

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

We show that if $Ω \subset R^{3}$ is a two-sided NTA domain with AD-regular boundary such that the logarithm of the Poisson kernel belongs to $VMO (σ)$ , where $σ$ is th…

math.CA2016

Absolute continuity of harmonic measure for domains with lower regular boundaries

Murat Akman, Jonas Azzam, Mihalis Mourgoglou

We study absolute continuity of harmonic measure with respect to surface measure on domains $Ω$ that have large complements. We show that if $Γ \subset R^{d + 1}$ is $d$ -Ahlf…

math.CA2016

Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability

Jonas Azzam, Mihalis Mourgoglou, Xavier Tolsa

We show that, for disjoint domains in the Euclidean space whose boundaries satisfy a non-degeneracy condition, mutual absolute continuity of their harmonic measures implies absolut…

math.CA2016

Approximate tangents, harmonic measure, and domains with rectifiable boundaries

Mihalis Mourgoglou

Let $Ω \subset R^{n + 1}$ , $n \geq 1$ , be an open and connected set. Set $T_{n}$ to be the set of points $ξ \in \partial Ω$ so that there exists an approximate tangent…

Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions

Uniform rectifiability, elliptic measure, square functions, and ε-approximability via an ACF monotonicity formula

On a two-phase problem for harmonic measure in general domains

Non-homogeneous square functions on general sets: suppression and big pieces methods

The one-phase problem for harmonic measure in two-sided NTA domains

Absolute continuity of harmonic measure for domains with lower regular boundaries

Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability

Approximate tangents, harmonic measure, and domains with rectifiable boundaries

Uniform rectifiability from Carleson measure estimates and $ε$ -approximability of bounded harmonic functions

Uniform rectifiability, elliptic measure, square functions, and $ε$ -approximability via an ACF monotonicity formula