On the renormalized volumes for conformally compact Einstein manifolds

P. Yang; S. Yu A. Chang; J. Qing

doi:10.1007/s10958-008-0094-0

On the renormalized volumes for conformally compact Einstein manifolds

Mathematics

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Abstract

We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the Q-curvature.

Original language	English (US)
Pages (from-to)	1755-1769
Number of pages	15
Journal	Journal of Mathematical Sciences (United States)
Volume	149
Issue number	6
DOIs	https://doi.org/10.1007/s10958-008-0094-0
State	Published - Mar 2008

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-008-0094-0

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title = "On the renormalized volumes for conformally compact Einstein manifolds",

abstract = "We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the Q-curvature.",

author = "P. Yang and Chang, \{S. Yu A.\} and J. Qing",

note = "Funding Information: This work was supported by NSF Grant DMS–0245266 and, in part, by NSF Grant DMS–0103160.",

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doi = "10.1007/s10958-008-0094-0",

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AU - Yang, P.

AU - Chang, S. Yu A.

AU - Qing, J.

N1 - Funding Information: This work was supported by NSF Grant DMS–0245266 and, in part, by NSF Grant DMS–0103160.

PY - 2008/3

Y1 - 2008/3

N2 - We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the Q-curvature.

AB - We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the Q-curvature.

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UR - https://www.scopus.com/pages/publications/40549095379#tab=citedBy

U2 - 10.1007/s10958-008-0094-0

DO - 10.1007/s10958-008-0094-0

M3 - Article

AN - SCOPUS:40549095379

SN - 1072-3374

VL - 149

SP - 1755

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JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

IS - 6

ER -

On the renormalized volumes for conformally compact Einstein manifolds

Abstract

All Science Journal Classification (ASJC) codes

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