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Dynamics and Rigidity of the Morse Boundary.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Dynamics and Rigidity of the Morse Boundary./
作者:	Liu, Qing.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	84 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
Contained By:	Dissertations Abstracts International82-12B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28419752
ISBN:	9798515256364

Dynamics and Rigidity of the Morse Boundary.
Liu, Qing.

Dynamics and Rigidity of the Morse Boundary. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 84 p.

Source: Dissertations Abstracts International, Volume: 82-12, Section: B.

Thesis (Ph.D.)--Brandeis University, 2021.

This item must not be sold to any third party vendors.

Let X be a proper geodesic metric space and let G be a group of isometries of X which acts geometrically. Cordes constructed the Morse boundary of X which generalizes the contracting boundary for CAT(0) spaces and the visual boundary for hyperbolic spaces. For the first part, we characterize Morse elements in G by their fixed points on the Morse boundary ∂MX. The dynamics on the Morse boundary is very similar to that of a δ-hyperbolic space. In particular, we show that the action of G on ∂MX is minimal if G is not virtually cyclic. We also get a uniform convergence result on the Morse boundary which gives us a weak north-south dynamics for a Morse isometry. This generalizes the work of Murray in the case of the contracting boundary of a CAT(0) space. For the second part, we investigate additional structures on the Morse boundary which determine the space up to a quasi-isometry. We prove that a homeomorphism between the Morse boundaries of two proper, cocompact spaces is induced by a quasi-isometry if and only if both the homeomorphism and its inverse are biholder, or quasisymmetric, or strongly quasi-conformal.

ISBN: 9798515256364Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Dynamics

Dynamics and Rigidity of the Morse Boundary.
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245 1 0 $a Dynamics and Rigidity of the Morse Boundary.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 84 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
500 $a Advisor: Charney, Ruth.
502 $a Thesis (Ph.D.)--Brandeis University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Let X be a proper geodesic metric space and let G be a group of isometries of X which acts geometrically. Cordes constructed the Morse boundary of X which generalizes the contracting boundary for CAT(0) spaces and the visual boundary for hyperbolic spaces. For the first part, we characterize Morse elements in G by their fixed points on the Morse boundary ∂MX. The dynamics on the Morse boundary is very similar to that of a δ-hyperbolic space. In particular, we show that the action of G on ∂MX is minimal if G is not virtually cyclic. We also get a uniform convergence result on the Morse boundary which gives us a weak north-south dynamics for a Morse isometry. This generalizes the work of Murray in the case of the contracting boundary of a CAT(0) space. For the second part, we investigate additional structures on the Morse boundary which determine the space up to a quasi-isometry. We prove that a homeomorphism between the Morse boundaries of two proper, cocompact spaces is induced by a quasi-isometry if and only if both the homeomorphism and its inverse are biholder, or quasisymmetric, or strongly quasi-conformal.
590 $a School code: 0021.
650 4 $a Mathematics. $3 515831
653 $a Dynamics
653 $a Hyperbolic space
653 $a Morse boundary
653 $a Quasi-conformal
690 $a 0405
710 2 $a Brandeis University. $b Mathematics. $3 1285724
773 0 $t Dissertations Abstracts International $g 82-12B.
790 $a 0021
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28419752