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Point derivations for Lipschitz functions andClarke's generalized derivative

Vladimir Demyanov, Diethard Pallaschke (1997)

Applicationes Mathematicae

Clarke’s generalized derivative f 0 ( x , v ) is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed x ∈ X and fixed v ∈ E the function f 0 ( x , v ) is continuous and sublinear in f ∈ L i p ( X , d ) . It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz’s product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.

Polar lattices from the point of view of nuclear spaces.

Wojciech Banaszczyk (1989)

Revista Matemática de la Universidad Complutense de Madrid

The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.

Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces

François Fillastre (2007)

Annales de l’institut Fourier

A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly). The induced metric on a convex Fuchsian polyhedron is isometric to a hyperbolic metric with conical singularities of positive singular curvature on a compact surface of genus greater than one. We prove that these metrics are actually realised by exactly one convex...

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