Geodesic
A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature
Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2137-2173.

Voir la notice de l'article provenant de la source EMS Press

In this paper we consider Riemannian manifolds (Mn,g) of dimension n≥5, with semi-positive Q-curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green's function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive Q-curvature. Modifying the test function construction of Esposito-Robert, we show that it is possible to choose an initial conformal metric so that the flow has a sequential limit which is smooth and positive, and defines a conformal metric of constant positive Q-curvature.
DOI : 10.4171/jems/553
Classification : 35-XX
Keywords: Q-curvature, Paneitz operator, conformal geometry, non-local flow 
@article{JEMS_2015_17_9_a2,
     author = {Matthew J. Gursky and Andrea Malchiodi},
     title = {A strong maximum principle for the {Paneitz} operator and a non-local flow for the $Q$-curvature},
     journal = {Journal of the European Mathematical Society},
     pages = {2137--2173},
     publisher = {mathdoc},
     volume = {17},
     number = {9},
     year = {2015},
     doi = {10.4171/jems/553},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/553/}
}
TY  - JOUR
AU  - Matthew J. Gursky
AU  - Andrea Malchiodi
TI  - A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature
JO  - Journal of the European Mathematical Society
PY  - 2015
SP  - 2137
EP  - 2173
VL  - 17
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/553/
DO  - 10.4171/jems/553
ID  - JEMS_2015_17_9_a2
ER  - 
%0 Journal Article
%A Matthew J. Gursky
%A Andrea Malchiodi
%T A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature
%J Journal of the European Mathematical Society
%D 2015
%P 2137-2173
%V 17
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/553/
%R 10.4171/jems/553
%F JEMS_2015_17_9_a2
Matthew J. Gursky; Andrea Malchiodi. A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature. Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2137-2173. doi : 10.4171/jems/553. http://geodesic.mathdoc.fr/articles/10.4171/jems/553/

Cité par Sources :