Geometric growth on translation surfaces
The thesis was published by
Colognese, Paul,
in September 2021,
University of Warwick.
Abstract:
In this thesis we study geometric growth on translation surfaces. We obtain asymptotic formulae for the growth of various geometric objects on translation surfaces such as volumes of balls and circumferences of large circles. Using these asymptotic formulae, we then prove a distribution result for large circles on translation surfaces. Finally, we explore the entropy minimization problem for translation surfaces and prove a special case. These results generalize well-known results that hold for negatively curved surfaces.
The full thesis can be downloaded at :
http://wrap.warwick.ac.uk/167642/1/WRAP_Theses_Colognese_2021.pdf
http://wrap.warwick.ac.uk/167642/1/WRAP_Theses_Colognese_2021.pdf