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Quantitative Embeddability and Conne...

ProQuest Information and Learning Co.

Quantitative Embeddability and Connectivity in Metric Spaces.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Quantitative Embeddability and Connectivity in Metric Spaces./
Author:	Eriksson-Bique, Sylvester David.
Description:	1 online resource (267 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
Contained By:	Dissertation Abstracts International79-01B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355128277

Quantitative Embeddability and Connectivity in Metric Spaces.
Eriksson-Bique, Sylvester David.

Quantitative Embeddability and Connectivity in Metric Spaces. - 1 online resource (267 pages)

Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis studies three analytic and quantitative questions on doubling metric (measure) spaces. These results are largely independent and will be presented in separate chapters.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355128277Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Quantitative Embeddability and Connectivity in Metric Spaces.
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035 $a (MiAaPQ)AAI10261097
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035 $a AAI10261097
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Eriksson-Bique, Sylvester David. $3 1180630
245 1 0 $a Quantitative Embeddability and Connectivity in Metric Spaces.
264 0 $c 2017
300 $a 1 online resource (267 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
500 $a Adviser: Bruce Kleiner.
502 $a Thesis (Ph.D.) $c New York University $d 2017.
504 $a Includes bibliographical references
520 $a This thesis studies three analytic and quantitative questions on doubling metric (measure) spaces. These results are largely independent and will be presented in separate chapters.
520 $a The first question concerns representing metric spaces arising from complete Riemannian manifolds in Euclidean space. More precisely, we find bi-Lipschitz embeddings &fnof; for subsets A of complete Riemannian manifolds M of dimension n, where N could depend on a bound on the curvature and diameter of A. The main difficulty here is to control the distortion of such embeddings in terms of the curvature of the manifold. In constructing the embeddings, we will study the collapsing theory of manifolds in detail and at multiple scales. Similar techniques give embeddings for subsets of complete Riemannian orbifolds and quotient metric spaces.
520 $a The second part of the thesis answers a question about finding quantitative and weak conditions that ensure large families of rectifiable curves connecting pairs of points. These families of rectifiable curves are quantified in terms of Poincare inequalities. We identify a new quantitative connectivity condition in terms of curve fragments, which is equivalent to possessing a Poincare inequality with some exponent. The connectivity condition arises naturally in three different contexts, and we present methods to find Poincare inequalities for the spaces involved. In particular, we prove such inequalities for spaces with weak curvature bounds and thus resolve a question of Tapio Rajala.
520 $a In the final part of the thesis we study the local geometry of spaces admitting differentiation of Lipschitz functions with certain Banach space targets. The main result shows that such spaces can be characterized in terms of Poincare inequalities and doubling conditions. In fact, such spaces can be covered by countably many pieces, each of which is an isometric subset of a doubling metric measure space admitting a Poincare inequality. In proving this, we will find a new way to use hyperbolic fillings to enlarge certain sub-sets into spaces admitting Poincare inequalities.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a New York University. $b Mathematics. $3 1180487
773 0 $t Dissertation Abstracts International $g 79-01B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10261097 $z click for full text (PQDT)

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