Construction de surfaces à courbure moyenne constante et surfaces minimales par des méthodes perturbatives

Abstract : The subject of this thesis is the study of minimal and constant mean curvature submanifolds and of the influence of the geometry of the ambient manifold on the solutions of this problem.In the first chapter, following the ideas of F. Almgren, we propose a generalization of the notion of hypersurface with constant mean curvature to all codimensions. In codimension n-k we define constant mean curvature submanifolds as the critical points of the functional of the k - dimensional volume of the boundaries of k+1 - dimensional minimal submanifolds. We prove the existence in compact n-dimensional manifolds of n-k codimensional submanifolds with constant mean curvature for all k
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Tatiana Zolotareva. Construction de surfaces à courbure moyenne constante et surfaces minimales par des méthodes perturbatives. Equations aux dérivées partielles [math.AP]. Université Paris-Saclay, 2016. Français. ⟨NNT : 2016SACLX003⟩. ⟨tel-01312173⟩

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