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Uniformly Convex Metric Spaces

Martin Kell (2014)

Analysis and Geometry in Metric Spaces

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvex topology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-space with weak topology which is not Hausdorff is given. In the end existence and uniqueness...

Uniqueness of Kähler-Einstein cone metrics.

Thalia D. Jeffres (2000)

Publicacions Matemàtiques

The purpose of this paper is to describe a method to construct a Kähler metric with cone singularity along a divisor and to illustrate a type of maximum principle for these incomplete metrics by showing that Kähler-Einstein metrics are unique in geometric Hölder spaces.

Uniqueness of the stereographic embedding

Michael Eastwood (2014)

Archivum Mathematicum

The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.

Uniqueness results for the Minkowski problem extended to hedgehogs

Yves Martinez-Maure (2012)

Open Mathematics

The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere 𝕊 n of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.

Unit tangent sphere bundles with constant scalar curvature

Eric Boeckx, Lieven Vanhecke (2001)

Czechoslovak Mathematical Journal

As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.

Unit vector fields on antipodally punctured spheres: big index, big volume

Fabiano G. B. Brito, Pablo M. Chacón, David L. Johnson (2008)

Bulletin de la Société Mathématique de France

We establish in this paper a lower bound for the volume of a unit vector field v → defined on 𝐒 n ∖ { ± x } , n = 2 , 3 . This lower bound is related to the sum of the absolute values of the indices of v → at x and - x .

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