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For the past forty years, Robert Bartnik has been one of the
leading mathematicians working on mathematical general relativity
and geometric analysis. Since his early dissertation work on the
existence of maximal hypersurfaces in general asymptotically flat
spacetimes, done under the guidance of S.T. Yau at the Institute
for Advanced Study at Princeton, Bartnik's work has had a major
impact on a number of different areas in mathematical relativity.
His careful definition of the ADM mass on asymptotically Euclidean
geometries, together with his analysis of the Laplace operator on
such geometries, has been highly influential in geometric analysis.
This work led in turn to his insightful definition of ""quasi-local
mass,"" a topic of intense interest to this day. Bartnik's
collaboration with his student John McKinnon resulted in their
iconic discovery of a globally regular static solution of the
Einstein-Yang-Mills equations. His proof that there exist globally
hyperbolic spacetime solutions of Einstein's equations, which
contain no constant mean curvature Cauchy surfaces, was very
surprising, and has led to a variety of further results of this
nature. The procedure he developed for generating solutions of the
Einstein constraint equations using a parabolic PDE system, has
already led to important applications and is likely to be very
useful in the future. With the publication of this volume, the
editors wish to honor Robert Bartnik's great contributions to their
field. Included in this collection are most of his published
papers, together with short essays by friends and colleagues who
have been strongly influenced by him. The editors dedicate this
collection to Robert, and to all those who will greatly benefit
from being introduced to his work.
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