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Big groups of automorphisms of some Klein surfaces.

Beata Mockiewicz (2002)

RACSAM

Sea Xp una superficie de Klein compacta con borde de gen algebraico p ≥ 2. Se sabe que si G es un grupo de automorfismos de Xp entonces |G| ≤ 12(p- 1). Se dice que G es un grupo grande de gen p si |G| > 4(p -1). En el presente artículo se halla una familia de enteros p para los que el único grupo grande de gen p son los grupos diédricos. Esto significa que, en términos del gen real introducido por C. L. May, para tales valores de p no existen grupos grandes de gen real p.

Bilipschitz embeddings of metric spaces into euclidean spaces.

Stephen Semmes (1999)

Publicacions Matemàtiques

When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small ("snowflake") deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, like rectifiability, differentiability, and curves of finite length. Here we discuss a (somewhat technical)...

Bilipschitz extensions from smooth manifolds.

Taneli Huuskonen, Juha Partanen, Jussi Väisälä (1995)

Revista Matemática Iberoamericana

We prove that every compact C1-submanifold of Rn, with or without boundary, has the bilipschitz extension property in Rn.

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