Related papers: Scalar curvature, flat Borromean rings, and the 3-…

We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.

We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…

We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations.…

We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries

We consider the 3-body problem of celestial mechanics in Euclidean, elliptic, and hyperbolic spaces, and study how the Lagrangian (equilateral) relative equilibria bifurcate when the Gaussian curvature varies. We thus prove the existence of…

We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…

This is a problem list in the theory of foliations and laminations of 3-manifolds. The focus is on the relationship of foliations and laminations with other aspects of 3-manifold topology, especially with the Thurston theory of geometric…

[This is an expository article. I have submitted it to the American Mathematical Monthly.] The three-body problem defines a dynamics on the space of triangles in the plane. The shape sphere is the moduli space of oriented similarity classes…

This monograph describes a Riemannian geometric reduction approach to the three-body problem. The fundamental theorems are presented in the introductory part, whereas their proofs are provided in later chapters where specific topics are…

A book, concerning the classical restricted three body problem, and the approach to this old conundrum coming from the modern methods of symplectic and contact geometry. It is split into Part I (theoretical aspects), and Part II (practical…

This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass…

This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston's geometrization conjecture. The sequences are minimizing sequences for a certain (optimal) scalar-curvature…

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…

A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…

First, recent work on light scalar mesons, which is of possible interest in connection with the strong coupling region of QCD is briefly discussed. Then a very short highlighting of a paper concerned with an application to the eta -> 3 pi…

Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…

The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…

This article is a survey of recent results about scalar curvature and contractible open $3$-manifolds. It is dedicated to the memory of Professor S. S. Chern.

These lecture notes give a very short introduction to coarsening phenomena and summarize some recent results in the field. They focus on three aspects: the super-universality hypothesis, the geometry of growing structures, and coarsening in…