Harmonic measure on sets of codimension larger than one
نویسندگان
چکیده
منابع مشابه
Continuous Leafwise Harmonic Functions on Codimension One Transversely Isometric Foliations
Let F be a codimension one foliation on a closed manifold M which admits a transverse dimension one Riemannian foliation. Then any continuous leafwise harmonic functions are shown to be constant on leaves.
متن کاملHarmonic Measure and Polynomial Julia Sets
There is a natural conjecture that the universal bounds for the dimension spectrum of harmonic measure are the same for simply connected and for non-simply connected domains in the plane. Because of the close relation to conformal mapping theory, the simply connected case is much better understood, and proving the above statement would give new results concerning the properties of harmonic meas...
متن کاملDimension of the harmonic measure of non-homogeneous Cantor sets
We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets as a continuous function of the parameters determining these sets. This results extend a previous one of the author and do not use ergodic theoretic tools, not applicable to our case.
متن کاملSingular Sets for Harmonic Measure on Locally Flat Domains with Locally Finite Surface Measure
A theorem of David and Jerison asserts that harmonic measure is absolutely continuous with respect to surface measure in NTA domains with Ahlfors regular boundaries. We prove that this fails in high dimensions if we relax the Ahlfors regularity assumption by showing that, for each d > 1, there exists a Reifenberg flat domain Ω ⊂ R with H(∂Ω) < ∞ and a subset E ⊂ ∂Ω with positive harmonic measur...
متن کاملCodimension One Symplectic Foliations
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2017
ISSN: 1631-073X
DOI: 10.1016/j.crma.2017.02.013