We define Strebel differentials for stable complex curves, prove the existence and uniqueness theorem that generalizes Strebel’s theorem for smooth curves, and show how this construction can be applied to clarify a delicate point in Kontsevich’s proof of Witten’s conjecture.

A global uniqueness theorem for stationary black holes is proved as a direct consequence of the Topological Censorship Theorem and the topological classification of compact, simply connected four-manifolds.

A uniqueness theorem for Minkowski space and de Sitter space associated with the occurrence of null lines (inextendible globally achronal null geodesics) is presented. This result is obtained as a consequence of the null splitting theorem, which is also discussed.

where W is a standard d-dimensional Brownian motion on a probability space (Ω,F , (Ft)0≤t≤T , P ) with (Ft)0≤t≤T the filtration generated by W . The function g : Ω × [0, T ] × R × R → R is called generator of (1.1). Here T is the terminal time, and ξ is a R-valued FT -adapted random variable; (g, T, ξ) are the parameters of (1.1). The solution (yt, zt)t∈[0,T ] is a pair of Ft-adapted and square...

We review the mathematics of the theory of entanglement measures. As well as giving proofs from first principles for some well-known and important results, we provide a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem o...

A uniqueness theorem for an LU decomposition of a totally nonnegative matrix is obtained.

In this paper, we prove a uniqueness theorem for a.elass of eomplementari~ problems involving M-matrices.