%0 PDF
%T A Theory of Sub-Finsler Surface Area in the Heisenberg Group
%A Sánchez, Andrew.
%D 2017-06-29T09:04:37.223-04:00
%8 2017-07-07
%R http://localhost/files/p8419060s
%X Abstract: This work is concerned with the metric properties of continuous
Heisenberg group under Carnot-Caratheodory metrics. Such metrics are in general
sub-Finsler, but a particular choice of CC-metric yields the sub-Riemannian case, which has
long been studied by analysts and geometers alike. In the sub-Riemannian case, there is a
clear definition of surface area that can be easily expressed and computed. This thesis is
a comprehensive study of surface area in general for the previously unstudied sub-Finsler
cases, and proposes four inequivalent definitions of surface area based on Minkowski
content that agree in the sub-Riemannian setting. A still-open conjecture by Pansu in the
sub-Riemannian case is concerned with maximizing the the isoperimetric ratio (Volume)^(3/4)
/ (Surface area). Included in this thesis is a study of this isoperimetric problem in
sub-Finsler cases using the theory of surface area established within, with bounds on the
isoperimetric constants for the four notions, computed examples yielding best known
constants in the CC-metrics that arise from the L-1 and L-Infinity norms, and theorems
concerning first variation of perimeter and mean curvature.; Thesis (Ph.D.)--Tufts University, 2017.; Submitted to the Dept. of Mathematics.; Advisor: Moon Duchin.; Committee: Kim Ruane, Fulton Gonzalez, and Luca Capogna.; Keyword: Mathematics.
%[ 2022-10-11
%9 Text
%~ Tufts Digital Library
%W Institution