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Riemannian approximation in Carnot groups

Published online by Cambridge University Press:  06 September 2021

András Domokos
Affiliation:
Department of Mathematics and Statistics, California State University Sacramento, 6000 J Street, Sacramento, CA 95819, USA ([email protected])
Juan J. Manfredi
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA ([email protected])
Diego Ricciotti
Affiliation:
Department of Mathematics and Statistics, California State University Sacramento, 6000 J Street, Sacramento, CA 95819, USA ([email protected])

Abstract

We present self-contained proofs of the stability of the constants in the volume doubling property and the Poincaré and Sobolev inequalities for Riemannian approximations in Carnot groups. We use an explicit Riemannian approximation based on the Lie algebra structure that is suited for studying nonlinear subelliptic partial differential equations. Our approach is independent of the results obtained in [11].

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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