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We prove that there exists a class of non-stationary solutions to the Einstein-Euler equations which have a Newtonian limit. The proof of this result is based on a symmetric hyperbolic formulation of… (More)

We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein-Yang-Mills equations for an arbitrary compact semisimple gauge group in the so-called regular case.… (More)

We study Ricci flows on R, n ≥ 3, that evolve from rotationally symmetric, asymptotically flat initial data containing no embedded minimal hyperspheres. We show that in this case the flow is… (More)

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or… (More)

We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma models with… (More)

We prove local existence and uniqueness of static spherically symmetric solutions of the EinsteinYang-Mills equations for any action of the rotation group (or SU(2)) by automorphisms of a principal… (More)

We establish the existence of a wide class of inhomogeneous relativistic solutions to the Einstein–Euler equations that are well approximated on cosmological scales by solutions of Newtonian gravity.… (More)

We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein-Euler equations that have a Newtonian limit. This class includes solutions that represent a… (More)

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter $${\epsilon=v_T/c}$$$${(0< \epsilon <… (More)