Les applications conformes-harmoniques dʼune variété conforme de dimension 4 vers une variété riemannienne sont les solutions dʼune équation non linéaire, conformément invariante, dʼordre 4. Nous démontrons un résultat général dʼexistence pour ces applications conformes-harmoniques, analogue au théorème dʼEells–Sampson pour les applications harmoniques. La démonstration utilise un flot géométrique et sʼappuie sur des résultats de Gursky–Viaclovsky et Lamm.
Conformal harmonic maps from a 4-dimensional conformal manifold to a Riemannian manifold are maps satisfying a certain conformally invariant fourth order equation. We prove a general existence result for conformal harmonic maps, analogous to the Eells–Sampson theorem for harmonic maps. The proof uses a geometric flow and relies on results of Gursky–Viaclovsky and Lamm.
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@article{CRMATH_2012__350_21-22_967_0, author = {Biquard, Olivier and Madani, Farid}, title = {A construction of conformal-harmonic maps}, journal = {Comptes Rendus. Math\'ematique}, pages = {967--970}, publisher = {Elsevier}, volume = {350}, number = {21-22}, year = {2012}, doi = {10.1016/j.crma.2012.10.021}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2012.10.021/} }
TY - JOUR AU - Biquard, Olivier AU - Madani, Farid TI - A construction of conformal-harmonic maps JO - Comptes Rendus. Mathématique PY - 2012 SP - 967 EP - 970 VL - 350 IS - 21-22 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.10.021/ DO - 10.1016/j.crma.2012.10.021 LA - en ID - CRMATH_2012__350_21-22_967_0 ER -
%0 Journal Article %A Biquard, Olivier %A Madani, Farid %T A construction of conformal-harmonic maps %J Comptes Rendus. Mathématique %D 2012 %P 967-970 %V 350 %N 21-22 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.10.021/ %R 10.1016/j.crma.2012.10.021 %G en %F CRMATH_2012__350_21-22_967_0
Biquard, Olivier; Madani, Farid. A construction of conformal-harmonic maps. Comptes Rendus. Mathématique, Tome 350 (2012) no. 21-22, pp. 967-970. doi : 10.1016/j.crma.2012.10.021. http://www.numdam.org/articles/10.1016/j.crma.2012.10.021/
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