A note on renormalized volume functionals

Sun Yung Alice Chang; Hao Fang; C. Robin Graham

doi:10.1016/j.difgeo.2013.10.001

A note on renormalized volume functionals

Sun Yung Alice Chang, Hao Fang, C. Robin Graham

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compactification. The second variation of renormalized volume functionals under conformal change is identified, and is used to show that Einstein metrics of nonzero scalar curvature are local extrema.

Original language	English (US)
Pages (from-to)	246-258
Number of pages	13
Journal	Differential Geometry and its Application
Volume	33
DOIs	https://doi.org/10.1016/j.difgeo.2013.10.001
State	Published - Mar 2014

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology
Computational Theory and Mathematics

Keywords

Asymptotically hyperbolic Einstein metric
Renormalized volume functionals

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10.1016/j.difgeo.2013.10.001

Cite this

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title = "A note on renormalized volume functionals",

abstract = "New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compactification. The second variation of renormalized volume functionals under conformal change is identified, and is used to show that Einstein metrics of nonzero scalar curvature are local extrema.",

keywords = "Asymptotically hyperbolic Einstein metric, Renormalized volume functionals",

author = "Chang, {Sun Yung Alice} and Hao Fang and Graham, {C. Robin}",

year = "2014",

month = mar,

doi = "10.1016/j.difgeo.2013.10.001",

language = "English (US)",

volume = "33",

pages = "246--258",

journal = "Differential Geometry and its Application",

issn = "0926-2245",

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T1 - A note on renormalized volume functionals

AU - Chang, Sun Yung Alice

AU - Fang, Hao

AU - Graham, C. Robin

PY - 2014/3

Y1 - 2014/3

N2 - New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compactification. The second variation of renormalized volume functionals under conformal change is identified, and is used to show that Einstein metrics of nonzero scalar curvature are local extrema.

AB - New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compactification. The second variation of renormalized volume functionals under conformal change is identified, and is used to show that Einstein metrics of nonzero scalar curvature are local extrema.

KW - Asymptotically hyperbolic Einstein metric

KW - Renormalized volume functionals

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DO - 10.1016/j.difgeo.2013.10.001

M3 - Article

AN - SCOPUS:84895905235

SN - 0926-2245

VL - 33

SP - 246

EP - 258

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -

A note on renormalized volume functionals

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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