Smooth Finsler metrics are a natural generalization of Riemannian ones and have been widely studied in the framework of differential geometry. The definition can be weakened by allowing the metric to be only Borel measurable. This generalization is necessary in view of applications, such as, for instance, optimization problems. In this paper we show that smooth Finsler metrics are dense in Bore...

We analyse symmetry breaking in general gauge theories paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: a Euclidean metric associated with the scalar sector, and another generally inequivalent metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of th...

Natural metrics in the hyperbolic α-Bloch-, weighted Dirichletand Qp-classes are introduced, and these classes are shown to be complete metric spaces with respect to the corresponding metrics. Then Lipschitz continuous and compact composition operators Cφ(f) = f ◦φ acting from the hyperbolic α-Bloch-class to the hyperbolic weighted Dirichletor Qp-class are characterized by conditions depending ...

INTRODUCTION Last April 1, Google launched Google Scholar Metrics, a new tool that provides impact metrics for scientific journals, measured from citation counts. The research community was caught on guard and many wondered whether it was a real product or just a joke (April 1 is Fools' Day). However, to the delight of bibliometricians and uneasiness of some major scientific publishers, the Goo...

Abstract. We show that for each weakly majorizing measure there is a natural metric with respect to which sample paths of stochastic processes are Hölder continuous and their Hölder norm satisfies a strong integrability condition. We call such metric a minorizing metric. The class of minorizing metrics is minimal among all metrics assuring sample Hölder continuity of processes satisfying certai...

On the manifold M(M) of all Riemannian metrics on a compact manifold M one can consider the natural L-metric as described first by [11]. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a conditio...

On the manifold M(M) of all Riemannian metrics on a compact manifold M one can consider the natural L-metric as decribed first by [10]. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition...

We compute the asymptotic metrics for moduli spaces of SU(N) monopoles with maximal symmetry breaking. These metrics are exponentially close to the exact monopole metric 1 as soon as, for each simple root, the individual monopoles corresponding to that root are well separated. We also show that the estimates can be differentiated term by term in natural coordinates, which is a new result even f...

We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbativ...