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thesisfinal.pdf (237.53 KB)
ETD Abstract Container
Abstract Header
Quasiconformal maps on a 2-step Carnot group
Author Info
Gardiner, Christopher James
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1498487423057279
Abstract Details
Year and Degree
2017, Master of Arts (MA), Bowling Green State University, Mathematics.
Abstract
In this paper, we find all the quasiconformal maps on a particular non-rigid 2-step Carnot group. In particular, all quasiconformal maps on this Carnot group preserve the vertical direction. Given that a Carnot group is a Lie algebra with a group structure, we employ concepts from linear algebra and abstract algebra to gain information about the group. Utilizing the theory of Pansu differentiability along with the biLipschitz nature of quasisymmetric maps, we use an analytical approach to help determine the form of any quasiconformal map on the Carnot group. The main result has consequences for the rigidity of quasiisometries of negatively curved solvable Lie groups.
Committee
Xiangdong Xie (Advisor)
Kit Chan (Committee Member)
Pages
34 p.
Subject Headings
Mathematics
Keywords
Algebra
;
Linear algebra
;
Analysis
;
Calculus
;
Lie algebra
;
Carnot group
;
Quasiconformal
;
Quasisymmetric
;
biLipschitz
;
Pansu differentiability
;
graded isomorphism
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Citations
Gardiner, C. J. (2017).
Quasiconformal maps on a 2-step Carnot group
[Master's thesis, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1498487423057279
APA Style (7th edition)
Gardiner, Christopher.
Quasiconformal maps on a 2-step Carnot group.
2017. Bowling Green State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1498487423057279.
MLA Style (8th edition)
Gardiner, Christopher. "Quasiconformal maps on a 2-step Carnot group." Master's thesis, Bowling Green State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1498487423057279
Chicago Manual of Style (17th edition)
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Document number:
bgsu1498487423057279
Download Count:
549
Copyright Info
© 2017, some rights reserved.
Quasiconformal maps on a 2-step Carnot group by Christopher James Gardiner is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Bowling Green State University and OhioLINK.