Sökning: "Jonatan Vasilis"

Hittade 2 avhandlingar innehållade orden Jonatan Vasilis.

1. 1. Harmonic measures

   Författare :Jonatan Vasilis; Göteborgs universitet; []
   Nyckelord :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;

   Sammanfattning : 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. LÄS MER

3. 2. On the ring lemma

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

   Sammanfattning : 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. LÄS MER