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The Ricci flow on manifolds with bou...

Gianniotis, Panagiotis.

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The Ricci flow on manifolds with boundary.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Ricci flow on manifolds with boundary./
作者:	Gianniotis, Panagiotis.
面頁冊數:	84 p.
附註:	Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
Contained By:	Dissertation Abstracts International75-01B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3594670
ISBN:	9781303393495

The Ricci flow on manifolds with boundary.
Gianniotis, Panagiotis.

The Ricci flow on manifolds with boundary. - 84 p.

Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.

Thesis (Ph.D.)--State University of New York at Stony Brook, 2013.

In this thesis, we investigate issues related to boundary value problems for the Ricci flow.

ISBN: 9781303393495Subjects--Topical Terms:

515831
Mathematics.

The Ricci flow on manifolds with boundary.
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245 1 4 $a The Ricci flow on manifolds with boundary.
300 $a 84 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-01(E), Section: B.
500 $a Adviser: Michael Anderson.
502 $a Thesis (Ph.D.)--State University of New York at Stony Brook, 2013.
520 $a In this thesis, we investigate issues related to boundary value problems for the Ricci flow.
520 $a First, we focus on a compact manifold with boundary and show the short-time existence, regularity and uniqueness of the flow. To obtain these results we impose the boundary conditions proposed by Anderson for the Einstein equations, namely the mean curvature and the conformal class of the boundary. We also show that a certain continuation principle holds. Our methods still apply when the manifold is not compact, as long as it has compact boundary and an appropriate control of the geometry at infinity.
520 $a Secondly, motivated by the static extension conjecture in Mathematical General Relativity, we study a boundary value problem for the Ricci flow on warped products. We impose the boundary data proposed by Bartnik for the static vacuum equations, which are the mean curvature and the induced metric of the boundary of the base manifold.
520 $a We conclude the thesis applying the results above to study the flow on a 3-manifold with symmetry. We show the long time existence of the flow and study its behavior in different situations.
590 $a School code: 0771.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a State University of New York at Stony Brook. $b Mathematics. $3 2096807
773 0 $t Dissertation Abstracts International $g 75-01B(E).
790 $a 0771
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3594670