Comptes Rendus
Article de recherche - Géométrie et Topologie
Quantitative smoothing of polyhedral manifolds
[Lissage quantitatif de variétés polyédriques]
Spencer Cattalani1 orcid
1Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 583-588

We use a recent result of C. Lange to obtain a converse to a theorem of B. Bowditch in dimension at most $4$. In particular, we show that, for $n \le 4$, a polyhedral $n$-manifold $X$ with bounded geometry is $K$-bi-Lipschitz homeomorphic to a Riemannian manifold $M$. We bound the constant $K$, the curvature, and the injectivity radius of $M$ by the bounds on the geometry of $X$.

Nous utilisons un résultat récent de C. Lange pour établir une réciproque d’un théorème de B. Bowditch en dimension au plus $4$. En particulier, nous montrons que, pour $n \le 4$, une variété polyédrique $X$ de dimension $n$ à géométrie bornée est homéomorphe par une application $K$-bi-lipschitzienne à une variété riemannienne $M$. Nous majorons la constante $K$, la courbure et le rayon d’injectivité de $M$ en fonction des bornes sur la géométrie de $X$.

Reçu le :
Révisé le :
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Publié le :
DOI : 10.5802/crmath.845
Classification : 57R12, 52B70
Keywords: Quantitative smoothing, polyhedral manifold, bi-Lipschitz map
Mots-clés : Lissage quantitatif, variété polyédrique, application bi-Lipschitz

Spencer Cattalani  1

1 Department of Mathematics, Stony Brook University, Stony Brook, NY 11794, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Spencer Cattalani. Quantitative smoothing of polyhedral manifolds. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 583-588. doi: 10.5802/crmath.845
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     volume = {364},
     doi = {10.5802/crmath.845},
     language = {en},
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