We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, as...

This paper presents an extension of the Poincaré-Hopf theorem to generalized critical points of a function on a compact region with nonsmooth boundary, M , defined by a finite number of smooth inequality constraints. Given a function F M → , we define the generalized critical points of F over M , define the index for the critical point, and show that the sum of the indices of the critical point...

Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened assumptions seem physically reasonable and retain the key requirement of explicit background independence. For simplicity, we restrict attention to the case of...

This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions d q xt/dt q −Axt ft, xt, Gxt, t ∈ 0, T, and x0 gx x 0 , in a Banach space X, where 0 < q < 1. General existence and uniqueness theorem, which extends many previous results, are given.

We get a uniqueness theorem for a Robin type boundary value problem for the Laplace equation arising in Physical Geodesy in the context of the gravimetric determination of the geoid. The boundary is an oblate ellipsoid of revolution and we have uniqueness of solutions provided that its eccentricity is (approximately) less than 0.526428.

For the 1-dimensional Kuramoto–Sivashinsky equation with random forcing term, existence and uniqueness of solutions is proved. Then, the Markovian semigroup is well defined; its properties are analyzed, in order to provide sufficient conditions for existence and uniqueness of invariant measures for this stochastic equation. Finally, regularity results are obtained by means of Girsanov theorem.

We establish asymptotics and uniqueness (up to translation) of travelling waves for delayed 2D lattice equations with non-monotone birth functions. First, with the help of Ikehara’s Theorem, the a priori asymptotic behavior of travelling wave is exactly derived. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. These results complement earlier res...

A topological approach to identifying the “good” interpolant among the four distinct solutions to the first–order Hermite interpolation problem for planar quintic Pythagorean–hodograph curves is presented. An existence theorem is proved, together with a complete analysis of uniqueness/non– uniqueness properties. A simple formula for finding the “good” solution, without appealing to curve fairne...

Weknow that not all minimal projections inLp (1<p<∞) are unique (see [B. Shekhtman, L. Skrzypek, On the non-uniqueness ofminimal projections inLp spaces]).The aimof this paper is examine the connection of the Chalmers–Metcalf operator (introduced in [B.L. Chalmers, F.T. Metcalf, A characterization and equations for minimal projections and extensions, J. Oper. Theory 32 (1994) 31–46]) to the uni...

We study the Radon-Nikodym problem for approximately proper equivalence relations and more specifically the uniqueness of certain Gibbs states. One of our tools is a variant of the dimension group introduced in the study of AF algebras. As applications, we retrieve sufficient conditions for the uniqueness of traces on AF algebras and parts of the PerronFrobenius-Ruelle theorem.