arXiv subjects
Publications and source records attributed to L. Lemaire.
We give more precision on the regularity of the domain that is needed to have the monotonicity and symmetry results recently proved by Damascelli and Pacella, result concerning p-Laplace equations. For this purpose, we study the continuity and semicontinuity of some parameters linked with the moving hyperplane method.
Carrying further work of T.A. Crawford, we show that each component of the space of harmonic maps from the $2$-sphere to complex projective $2$-space of degree $d$ and energy $4 πE$ is a smooth closed submanifold of the space of all $C^j$ maps $(j \geq 2)$. We achieve this by showing that the Gauss transform which relates them to spaces of holomorphic maps of given degree and ramification index is {\bf smooth} and has {\bf injective differential}.