Search for dissertations about: "Jonatan Vasilis"

Found 2 swedish dissertations containing the words Jonatan Vasilis.

  1. 1. Harmonic measures

    University dissertation from Göteborg : Chalmers University of Technology

    Author : Jonatan Vasilis; Göteborgs universitet.; Gothenburg University.; [2010]
    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; regular tree; square root of the Poisson kernel; random walk; discrete minimal thinness; p-Laplace operator;

    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

  2. 2. On the ring lemma

    University dissertation from Göteborg : Chalmers University of Technology

    Author : Jonatan Vasilis; Göteborgs universitet.; Gothenburg University.; [2008]
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; ring lemma; circle packing; sphere packing; Apollonian; sphere packing; circle packing; Apollonian;

    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