Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An Obata singular theorem for stratified spaces
HTML articles powered by AMS MathViewer

by Ilaria Mondello PDF
Trans. Amer. Math. Soc. 370 (2018), 4147-4175 Request permission

Abstract:

Consider a stratified space with a positive Ricci lower bound on the regular set and no cone angle larger than $2\pi$. For such stratified space we know that the first non-zero eigenvalue of the Laplacian is larger than or equal to the dimension. We prove here an Obata rigidity result when the equality is attained: the lower bound of the spectrum is attained if and only if the stratified space is isometric to a spherical suspension. Moreover, we show that the diameter is at most equal to $\pi$, and it is equivalent for the diameter to be equal to $\pi$ and for the first non-zero eigenvalue of the Laplacian to be equal to the dimension. We finally give a consequence of these results related to the Yamabe problem. Consider an Einstein stratified space without cone angles larger than $2\pi$: if there is a metric conformal to the Einstein metric and with constant scalar curvature, then it is an Einstein metric as well. Furthermore, if its conformal factor is not a constant, then the space is isometric to a spherical suspension.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53A30, 58C40
  • Retrieve articles in all journals with MSC (2010): 53A30, 58C40
Additional Information
  • Ilaria Mondello
  • Affiliation: UPMC Université Paris 6, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586
  • Address at time of publication: Université Paris Est Créteil, UFR Sciences et Technologies, Laboratoire d’Analyse et Mathématiques Appliquées, 61, avenue du Gévéral de Gaulle, 94010 Créteil Cedex, France
  • Email: ilaria.mondello@u-pec.fr
  • Received by editor(s): February 1, 2016
  • Received by editor(s) in revised form: October 19, 2016
  • Published electronically: December 29, 2017
  • Additional Notes: This work was supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (reference: ANR-10-LABX-0098)
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 4147-4175
  • MSC (2010): Primary 53A30, 58C40
  • DOI: https://doi.org/10.1090/tran/7105
  • MathSciNet review: 3811523