We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres.
On montre que la différentiabilité du profil isopérimétrique est une condition très contraignante pour les variétés riemanniennes analytiques réelles. Par exemple, sous une hypothèse supplémentaire, ce n'est possible que si la variété est homéomorphe à une sphère.
Accepted:
Published online:
@article{CRMATH_2009__347_5-6_293_0,
author = {Grimaldi, Renata and Nardulli, Stefano and Pansu, Pierre},
title = {Differentiability of the isoperimetric profile and topology of analytic {Riemannian} manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {293--297},
publisher = {Elsevier},
volume = {347},
number = {5-6},
year = {2009},
doi = {10.1016/j.crma.2009.01.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.003/}
}
TY - JOUR AU - Grimaldi, Renata AU - Nardulli, Stefano AU - Pansu, Pierre TI - Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds JO - Comptes Rendus. Mathématique PY - 2009 SP - 293 EP - 297 VL - 347 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.01.003/ DO - 10.1016/j.crma.2009.01.003 LA - en ID - CRMATH_2009__347_5-6_293_0 ER -
%0 Journal Article %A Grimaldi, Renata %A Nardulli, Stefano %A Pansu, Pierre %T Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds %J Comptes Rendus. Mathématique %D 2009 %P 293-297 %V 347 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.01.003/ %R 10.1016/j.crma.2009.01.003 %G en %F CRMATH_2009__347_5-6_293_0
Grimaldi, Renata; Nardulli, Stefano; Pansu, Pierre. Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 293-297. doi : 10.1016/j.crma.2009.01.003. http://www.numdam.org/articles/10.1016/j.crma.2009.01.003/
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Cited by Sources:
☆ Partially supported by Projet “Internazionalizzazione” “Propriètà asintotiche di varietà e di gruppi discreti” of Miur of Italy.
