NDLI: Parabolic constructions of asymptotically flat 3-metrics of prescribed scalar curvature

Content Provider	Springer Nature Link
Author	Lin, Chen Yun
Copyright Year	2013
Abstract	In 1993, Bartnik (J. Differ. Geom. 37(1):37–71) introduced a quasi-spherical construction of metrics of prescribed scalar curvature on 3-manifolds. Under quasi-spherical ansatz, the problem is converted into the initial value problem for a semi-linear parabolic equation of the lapse function. The original ansatz of Bartnik started with a background foliation with round metrics on the 2-sphere leaves. This has been generalized by several authors (Shi and Tam in J. Differ. Geom. 62(1):79–125, 2002; Smith in Gen. Relat. Gravit. 41(5):1013–1024, 2009; Smith and Weinstein in Commun. Anal. Geom. 12(3):511–551, 2004) under various assumptions on the background foliation. In this article, we consider background foliations given by conformal round metrics, and by the Ricci flow on 2-spheres. We discuss conditions on the scalar curvature function and on the foliation that guarantee the solvability of the parabolic equation, and thus the existence of asymptotically flat 3-metrics with a prescribed inner boundary. In particular, many examples of asymptotically flat-scalar flat 3-metrics with outermost minimal surfaces are obtained.
Starting Page	1309
Ending Page	1335
Page Count	27
File Format	PDF
ISSN	09442669
Journal	Calculus of Variations and Partial Differential Equations
Volume Number	49
Issue Number	3-4
e-ISSN	14320835
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-04-17
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Analysis Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Parabolic Constructions of Asymptotically Flat 3-metrics of Prescribed Scalar Curvature

Conformal metrics with prescribed Q-curvature on S n

Entire spacelike hypersurfaces of prescribed scalar curvature in Minkowski space

Parabolic stable surfaces with constant mean curvature

Rigidity of stable minimal hypersurfaces in asymptotically flat spaces

Killing graphs with prescribed mean curvature

On surfaces of prescribed weighted mean curvature

Hypersurfaces with constant anisotropic mean curvature in Riemannian manifolds

Perelman’s lambda-functional and the stability of Ricci-flat metrics

Parabolic constructions of asymptotically flat 3-metrics of prescribed scalar curvature

Similar Documents

Parabolic Constructions of Asymptotically Flat 3-metrics of Prescribed Scalar Curvature

Conformal metrics with prescribed Q-curvature on S n

Entire spacelike hypersurfaces of prescribed scalar curvature in Minkowski space

Parabolic stable surfaces with constant mean curvature

Rigidity of stable minimal hypersurfaces in asymptotically flat spaces

Killing graphs with prescribed mean curvature

On surfaces of prescribed weighted mean curvature

Hypersurfaces with constant anisotropic mean curvature in Riemannian manifolds

Perelman’s lambda-functional and the stability of Ricci-flat metrics

Parabolic constructions of asymptotically flat 3-metrics of prescribed scalar curvature