Einstein and conformally flat critical metrics of the volume functional

Authors:
Pengzi Miao and Luen-Fai Tam

Journal:
Trans. Amer. Math. Soc. **363** (2011), 2907-2937

MSC (2010):
Primary 53C20; Secondary 58JXX

DOI:
https://doi.org/10.1090/S0002-9947-2011-05195-0

Published electronically:
January 27, 2011

MathSciNet review:
2775792

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a constant. Let be the space of smooth metrics on a given compact manifold () with smooth boundary such that has constant scalar curvature and is a fixed metric on . Let be the volume of . In this work, we classify all Einstein or conformally flat metrics which are critical points of in .

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Additional Information

**Pengzi Miao**

Affiliation:
School of Mathematical Sciences, Monash University, Victoria, 3800, Australia

Address at time of publication:
Department of Mathematics, University of Miami, Coral Gables, Florida 33124

Email:
Pengzi.Miao@sci.monash.edu.au, pengzim@math.miami.edu

**Luen-Fai Tam**

Affiliation:
The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

Email:
lftam@math.cuhk.edu.hk

DOI:
https://doi.org/10.1090/S0002-9947-2011-05195-0

Received by editor(s):
January 7, 2009

Published electronically:
January 27, 2011

Additional Notes:
The first author was supported in part by Australian Research Council Discovery Grant #DP0987650

The second author was supported in part by Hong Kong RGC General Research Fund #CUHK403108

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.