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Menger curvature and Lipschitz parametrizations in metric spaces

Immo Hahlomaa (2005)

Fundamenta Mathematicae

We show that pointwise bounds on the Menger curvature imply Lipschitz parametrization for general compact metric spaces. We also give some estimates on the optimal Lipschitz constants of the parametrizing maps for the metric spaces in Ω(ε), the class of bounded metric spaces E such that the maximum angle for every triple in E is at least π/2 + arcsinε. Finally, we extend Peter Jones's travelling salesman theorem to general metric spaces.

Metric Ricci Curvature and Flow for PL Manifolds

Emil Saucan (2013)

Actes des rencontres du CIRM

We summarize here the main ideas and results of our papers [28], [14], as presented at the 2013 CIRM Meeting on Discrete curvature and we augment these by bringing up an application of one of our main results, namely to solving a problem regarding cube complexes.

Minimal length coset representatives for quotients of parabolic subgroups in Coxeter groups

Fabio Stumbo (2000)

Bollettino dell'Unione Matematica Italiana

In questo lavoro viene trovata un'espressione esplicita per i rappresentanti dei laterali di sottogrupi parabolici di gruppi di Coxeter aventi lunghezza minima: dato un sistema di Coxeter W , S ed un suo sottogruppo parabolico W I , I , con I S , si determina esplicitamente in ogni laterale W I w di W I un elemento avente lunghezza minima. Nella sezione 2 trattiamo i casi classici, i.e. W = A n , B n e D n . Dopo ciò, nella sezione 3, diamo una procedura per risolvere il problema nei restanti casi eccezionali, insieme a qualche...

Mini-programs for hidden lines on a surface

Josef Kateřiňák (1987)

Aplikace matematiky

Many programs for the hidden lines on a surface are known [1] but these programs are long and need a large memory of the computer. In this paper we show algorithms and the corresponding mini-program in BASIC which can be implemented on minicomputers with plotters or plotting displays. We map the surface in the parallel or central projections.

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