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Concept

Category of metric spaces

Related publications (8)

The (h, k)-Server Problem on Bounded Depth Trees

Marek Elias

We study the k-server problem in the resource augmentation setting, i.e., when the performance of the online algorithm with k servers is compared to the offline optimal solution with h

ASSOC COMPUTING MACHINERY2019

Supramenable groups

Julian Kellerhals

In this thesis we investigate the class of supramenable groups. In the first part we give an overview of some analogous characterizations of amenable and supramenable groups. This is followed by the study of two properties close to supramenability: megamen ...

EPFL2014

Actions of amenable equivalence relations on CAT(0) fields

Martin Anderegg, Philippe Paul Antoine Henry

We present the general notion of Borel fields of metric spaces and show some properties of such fields. Then we make the study specific to the Borel fields of proper CAT(0) spaces and we show that the standard tools we need behave in a Borel way. We also i ...

Cambridge University Press2014

Two and a half billion years of distance research

János Pach, Filip Moric

In a seminal paper published in 1946, Erd ̋os initiated the investigation of the distribution of distances generated by point sets in metric spaces. In spite of some spectacular par- tial successes and persistent attacks by generations of mathe- maticians, ...

2013

Tensors, Monads And Actions

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg-Moore category C^T that represents bimorphisms. The category of actions in C^T is then shown to be monadic over the base catego ...

Mount Allison University2013

Actions de relations d'équivalence sur les champs d'espaces métriques CAT(0)

Philippe Paul Antoine Henry

This work is dedicated to the study of Borel equivalence relations acting on Borel fields of CAT(0) metric spaces over a standard probability space. In this new framework we get similar results to some theorems proved recently by S. Adams-W. Ballmann or N. ...

EPFL2010

Moyennabilité et courbure : G-espaces boréliens et espaces CAT(0)

Martin Anderegg

As Avez showed (in 1970), the fundamental group of a compact Riemannian manifold of nonpositive sectional curvature has exponential growth if and only if it is not flat. After several generalizations from Gromov, Zimmer, Anderson, Burger and Shroeder, the ...

EPFL2010

Regularity in metric spaces

Serguei Timochine

Using arguments developed by De Giorgi in the 1950's, it is possible to prove the regularity of the solutions to a vast class of variational problems in the Euclidean space. The main goal of the present thesis is to extend these results to the more abstrac ...

EPFL2006

Related publications (8)

The (h, k)-Server Problem on Bounded Depth Trees

Marek Elias

We study the k-server problem in the resource augmentation setting, i.e., when the performance of the online algorithm with k servers is compared to the offline optimal solution with h

ASSOC COMPUTING MACHINERY2019