Nonlinear equations on Carnot groups and curvature problems for CR manifolds

Ermanno Lanconelli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2003)

  • Volume: 14, Issue: 3, page 227-238
  • ISSN: 1120-6330

Abstract

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We give a short overview of sub-Laplacians on Carnot groups starting from a result by Caccioppoli dated 1934. Then we show that sub-Laplacians on Carnot groups of step one arise in studying curvature problems for C ⁢ R manifolds. We restrict our presentation to the cases of the Webster-Tanaka curvature problem for the C ⁢ R sphere and of the Levi-curvature equation for strictly pseudoconvex functions.

How to cite

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Lanconelli, Ermanno. "Nonlinear equations on Carnot groups and curvature problems for CR manifolds." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.3 (2003): 227-238. <http://eudml.org/doc/252356>.

@article{Lanconelli2003,
abstract = {We give a short overview of sub-Laplacians on Carnot groups starting from a result by Caccioppoli dated 1934. Then we show that sub-Laplacians on Carnot groups of step one arise in studying curvature problems for $CR$ manifolds. We restrict our presentation to the cases of the Webster-Tanaka curvature problem for the $CR$ sphere and of the Levi-curvature equation for strictly pseudoconvex functions.},
author = {Lanconelli, Ermanno},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Hypoellipticity; Carnot groups; Sub-Laplacians; Webster-Tanaka curvature; Levi-curvature; hypoellipticity; sub-Laplacians},
language = {eng},
month = {9},
number = {3},
pages = {227-238},
publisher = {Accademia Nazionale dei Lincei},
title = {Nonlinear equations on Carnot groups and curvature problems for CR manifolds},
url = {http://eudml.org/doc/252356},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Lanconelli, Ermanno
TI - Nonlinear equations on Carnot groups and curvature problems for CR manifolds
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/9//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 3
SP - 227
EP - 238
AB - We give a short overview of sub-Laplacians on Carnot groups starting from a result by Caccioppoli dated 1934. Then we show that sub-Laplacians on Carnot groups of step one arise in studying curvature problems for $CR$ manifolds. We restrict our presentation to the cases of the Webster-Tanaka curvature problem for the $CR$ sphere and of the Levi-curvature equation for strictly pseudoconvex functions.
LA - eng
KW - Hypoellipticity; Carnot groups; Sub-Laplacians; Webster-Tanaka curvature; Levi-curvature; hypoellipticity; sub-Laplacians
UR - http://eudml.org/doc/252356
ER -

References

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