Some old and new results about rigidity of critical metric

Authors :: Gilles Carron
Laboratoire de Mathématiques Jean Leray (LMJL)
Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST)
Université de Nantes (UN)-Université de Nantes (UN)
ANR-10-BLAN-0105,ACG,Aspects Conformes de la Géométrie(2010)
Source :: Annali della Scuola Normale Superiore di Pisa, Annali della Scuola Normale Superiore di Pisa, 2014, Vol. XIII, (issue 4), pp.PP. 1091-1113
Publication Year :: 2014
Publisher :: Scuola Normale Superiore - Edizioni della Normale, 2014.
Abstract: We present a new proof of a recent ✏-regularity of G. Tian and J.Viaclovsky. Our idea also provides a new proof of a classical result of M. Anderson about volume rigidity of Einstein manifolds. Eventually, we also obtain new rigidity results for critical metrics.