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Intermediate Curvature, Spacetime Harmonic Functions and the Monotonicity of the Hawking Energy.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Intermediate Curvature, Spacetime Harmonic Functions and the Monotonicity of the Hawking Energy./
Author:	Hirsch, Sven.
Description:	1 online resource (172 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30311109click for full text (PQDT)
ISBN:	9798379572839

Intermediate Curvature, Spacetime Harmonic Functions and the Monotonicity of the Hawking Energy.
Hirsch, Sven.

Intermediate Curvature, Spacetime Harmonic Functions and the Monotonicity of the Hawking Energy. - 1 online resource (172 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--Duke University, 2023.

Includes bibliographical references

First, we introduce m-intermediate curvature Cm which interpolates between Ricci (m = 1) and scalar curvature (m = n − 1) and prove in this context a generalized Geroch conjecture. In particular, we show that Mn−m xTm, n ≤ 7, does not admit a metric with Cm > 0.Next, we study initial data sets (M, g, k) which are used in General Relativity to describe isolated gravitational systems. We introduce spacetime harmonic functions, i.e. functions solving the PDE ∆u = −trgk∣∇u∣, to give a new lower bound for the mass of (M, g, k). This lower bound in particular implies the spacetime positive mass theorem including the case of equality.Finally, we discuss recent progress towards the spacetime Penrose conjecture. We demonstrate how the famous monotonicity formula for the Hawking energy under inverse mean curvature flow can be generalized to initial data sets. This leads to a new notion of spacetime inverse mean curvature flow which is based on double null foliations.Several of the above results have been obtained in collaboration with Simon Brendle, Florian Johne, Demetre Kazaras, Marcus Khuri and Yiyue Zhang.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379572839Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

SpacetimeIndex Terms--Genre/Form:

542853
Electronic books.

Intermediate Curvature, Spacetime Harmonic Functions and the Monotonicity of the Hawking Energy.
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100 1 $a Hirsch, Sven. $3 3698276
245 1 0 $a Intermediate Curvature, Spacetime Harmonic Functions and the Monotonicity of the Hawking Energy.
264 0 $c 2023
300 $a 1 online resource (172 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Bray, Hubert.
502 $a Thesis (Ph.D.)--Duke University, 2023.
504 $a Includes bibliographical references
520 $a First, we introduce m-intermediate curvature Cm which interpolates between Ricci (m = 1) and scalar curvature (m = n − 1) and prove in this context a generalized Geroch conjecture. In particular, we show that Mn−m xTm, n ≤ 7, does not admit a metric with Cm > 0.Next, we study initial data sets (M, g, k) which are used in General Relativity to describe isolated gravitational systems. We introduce spacetime harmonic functions, i.e. functions solving the PDE ∆u = −trgk∣∇u∣, to give a new lower bound for the mass of (M, g, k). This lower bound in particular implies the spacetime positive mass theorem including the case of equality.Finally, we discuss recent progress towards the spacetime Penrose conjecture. We demonstrate how the famous monotonicity formula for the Hawking energy under inverse mean curvature flow can be generalized to initial data sets. This leads to a new notion of spacetime inverse mean curvature flow which is based on double null foliations.Several of the above results have been obtained in collaboration with Simon Brendle, Florian Johne, Demetre Kazaras, Marcus Khuri and Yiyue Zhang.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Astrophysics. $3 535904
650 4 $a Applied mathematics. $3 2122814
653 $a Spacetime
653 $a Harmonic functions
653 $a Hawking energy
653 $a Monotonicity
653 $a Intermediate curvature
655 7 $a Electronic books. $2 lcsh $3 542853
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690 $a 0596
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a Duke University. $b Mathematics. $3 1036449
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30311109 $z click for full text (PQDT)