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Search Results: 1 - 10 of 164309 matches for " Michael T. Anderson "
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Asymptotic behavior of future-complete cosmological space-times
Michael T. Anderson
Physics , 2003,
Abstract: This work discusses the apriori possible asymptotic behavior to the future, for (vacuum) space-times which are geodesically complete to the future and which admit a foliation by compact constant mean curvature Cauchy surfaces.
Orbifold compactness for spaces of Riemannian metrics and applications
Michael T. Anderson
Mathematics , 2003,
Abstract: This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such compactness for spaces of Bach-flat (for example half-conformally flat) metrics on 4-manifolds, and related results for metrics which are critical points of other natural Riemannian functionals on the space of metrics.
On the structure of conformally compact Einstein metrics
Michael T. Anderson
Mathematics , 2004,
Abstract: The main result of this paper is that the space of conformally compact Einstein metrics on a given manifold is a smooth, infinite dimensional Banach manifold, provided it is non-empty, generalizing earlier work of Graham-Lee and Biquard. We also prove full boundary regularity for such metrics in dimension 4, and a local existence and uniqueness theorem for such metrics with prescribed metric and stress-energy tensor at conformal infinity, again in dimension 4. This result also holds for Lorentzian-Einstein metrics with a positive cosmological constant.
Canonical metrics on 3-manifolds and 4-manifolds
Michael T. Anderson
Mathematics , 2005,
Abstract: We prove certain weak or idealized existence results for minimizers of the natural quadratic curvature functionals on the space of metrics on 4-manifolds. Overall, we try to exhibit the relations with the picture in 3-dimensions provided by Thurston geometrization. The existence results apply in particular to the structure of the moduli spaces of such metrics, and as such generalize most of the known results for moduli of Einstein metrics.
Unique continuation results for Ricci curvature and applications
Michael T. Anderson
Mathematics , 2005,
Abstract: Final version in paper linked above.
On the structure of asymptotically de Sitter and anti-de Sitter spaces
Michael T. Anderson
Mathematics , 2004,
Abstract: We discuss several aspects of the relation between asymptotically AdS and asymptotically dS spacetimes including: the continuation between these types of spaces, the global stability of asymptotically dS spaces and the structure of limits within this class, holographic renormalization, and the maximal mass conjecture of Balasubramanian-deBoer-Minic.
On the uniqueness and global dynamics of AdS spacetimes
Michael T. Anderson
Mathematics , 2006, DOI: 10.1088/0264-9381/23/23/021
Abstract: We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which is asymptotically stationary to the past and future is itself globally stationary. This gives certain rigidity or uniqueness results for exact AdS and related spacetimes.
Local rigidity of surfaces in space forms
Michael T. Anderson
Mathematics , 2007,
Abstract: This paper is withdrawn.
Boundary value problems for metrics on 3-manifolds
Michael T. Anderson
Mathematics , 2011,
Abstract: We discuss the problem of prescribing the mean curvature and conformal class as boundary data for Einstein metrics on 3-manifolds, in the context of natural elliptic boundary value problems for Riemannian metrics.
Alexandrov immersions, holonomy and minimal surfaces in $S^3$
Michael T Anderson
Mathematics , 2014,
Abstract: We prove that compact 3-manifolds $M$ of constant curvature +1 with boundary a minimal surface are locally naturally parametrized by the conformal class of the boundary metric $\gamma$ in the Teichmuller space of $\partial M$, when $genus(\partial M) \geq 2$. Stronger results are obtained in the case of genus 1 boundary, giving in particular a new proof of Brendle's solution of the Lawson conjecture. The results generalize to constant mean curvature surfaces, and surfaces in flat and hyperbolic 3-manifolds.
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