Reduction theory for mechanical systems with symmetry has its roots in the classical works
in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincaré, and others. The …

1. Introduction. Riemannian differential geometry originated in attempts to generalize the
highly successful theory of compact surfaces. From the earliest days, conformai changes of …

The book starts with a thorough introduction to connections and holonomy groups, and to
Riemannian, complex and Kähler geometry. Then the Calabi conjecture is proved and used …

We show that the mass of an asymptotically flat n‐manifold is a geometric invariant. The
proof is based on harmonic coordinates and, to develop a suitable existence theory, results …

We show that the coefficient γ (x) of the elliptic equation∇·(γ∇ u)= 0 in a two-dimensional
domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the …

Examples of edge operators include Laplacians on asymptotically flat and asymptotically
hyperbolic manifolds. Edge operators also arise in boundary problems around higher …

Hodge theory is a standard tool in characterizing differ-ential complexes and the topology of
manifolds. This book is a study of the Hodge-Kodaira and related decompositions on …

This paper gives a mathematically rigorous proof of the positive energy theorem using
spinors. This completes and simplifies the original argument presented by Edward Witten …

(1.1) Am+ K (x) u^ n+ 2Wn~ 2)= 0 in R", where A= V" d2/drf, and n> 3. This problem has its
root in Riemannian geometry. Let (M, g) be a Riemannian manifold of dimension s 3 and A" …

In this paper and its sequel we shall prove the local and then the global existence of
solutions of the classical Yang-Mills-Higgs equations in the temporal gauge. This paper …