Stability, complex-analyticity and constancy of pluriharmonic maps from compact Kaehler manifolds.
We study the stability of harmonic maps between Finsler manifolds and Riemannian manifolds with positive Ricci curvature, and we prove that if Mⁿ is a compact Einstein Riemannian minimal submanifold of a Riemannian unit sphere with Ricci curvature satisfying , then there is no non-degenerate stable harmonic map between M and any compact Finsler manifold.
We classify Hopf cylinders with proper mean curvature vector field in Sasakian 3-manifolds with respect to the Tanaka-Webster connection.
In Carnot groups of step ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.