Mathematical Research Letters

Volume 16 (2009)

Number 1

Singular Yamabe metrics and initial data with \emph{exactly} Kottler–Schwarzschild–de Sitter ends II. Generic metrics

Pages: 157 – 164



Piotr T. Chru\'sciel (Mathematical Institute and Hertford College, Oxford)

Frank Pacard (Université Paris Est and Institut Universitaire de France)

Daniel Pollack (University of Washington)


We present a gluing construction which adds, via a localized deformation, \emph{exactly Delaunay ends} to \emph{generic} metrics with constant positive scalar curvature. This provides time-symmetric initial data sets for the vacuum Einstein equations with positive cosmological constant with \emph{exactly} Kottler–Schwarzschild–de Sitter ends, extending the results in~\cite{ChPollack}.

Published 1 January 2009