Search for dissertations about: "Jonatan Vasilis"

Found 2 swedish dissertations containing the words Jonatan Vasilis.

  2. 1. Harmonic measures

    Author : Jonatan Vasilis; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; harmonic measure; square root of the Poisson kernel; Hardy space; p-Laplace operator; random walk; regular tree; discrete minimal thinness; Hardy space;

    Abstract : This thesis uses both analytic and probabilistic methods to study continuous and discrete problems. The main areas of study are the asymptotic properties of p-harmonic measure, and various aspects of the square root of the Poisson kernel. Fix a domain and a boundary point, subject to certain regularity conditions. READ MORE

  4. 2. On the ring lemma

    Author : Jonatan Vasilis; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; ring lemma; circle packing; sphere packing; Apollonian; sphere packing;

    Abstract : The sharp ring lemma states that if n ≥ 3 cyclically tangent discs with pairwise disjoint interiors are externally tangent to and surround the unit disc, then no disc has a radius below cn = (F2n-1 + F2n-2 - 1)-1 – where Fk denotes the kth Fibonacci number – and that the lower bound is attained in essentially unique Apollonian configurations. Here we give a proof by transforming the problem to a class of strip configurations, after which we closely follow a method of proof due to Aharonov and Stephenson. READ MORE