@article{c1341bf09afd4729b858e672b1b62b73,

title = "Sharp remainder of the poincar{\'E} inequality",

abstract = "In this paper, we obtain a sharp remainder formula for the Poincar{\'e} inequality which implies a simple proof of the sharp Poincar{\'e} inequality without using the variational principle. We also extend the idea to general Carnot groups. Thus, we have succeeded in finding a simple proof of the sharp Poincar{\'e} inequality in a more general case.",

author = "Tohru Ozawa and Durvudkhan Suragan",

note = "Funding Information: Received by the editors October 24, 2019. 2010 Mathematics Subject Classification. Primary 39B62, 39B99, 22E30. Key words and phrases. Poincar{\'e} inequality, sharp remainder, optimal constant, Heisenberg group, Carnot group. The authors were supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. No new data was collected or generated during the course of this research. Publisher Copyright: {\textcopyright} 2020 American Mathematical Society Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = oct,

doi = "10.1090/proc/15119",

language = "English",

volume = "148",

pages = "4235--4239",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "10",

}